In this thesis we investigate two operational models of name-passing calculi: one based on coalgebra, and one based on enriched automata. We develop a semantic framework for modelling the open bisimulation in π-calculus, hyperbisimulation in Fusion calculus, and the first semantic interpretation of FOλ(nabla) logic. We consider a category theoretic model where both “variables” and “names”, usually viewed as separate notions, are particular cases of the more general notion of atoms. The key aspect of this model is to consider functors over the category of irreflexive and symmetric finite relations. The models previously proposed for the separate notions of “variables” and “names” embed faithfully in the new one, and initial algebra/final coalgebra constructions can be transferred from the formers to the latter. Moreover, the new model admits a definition of distinction-aware simultaneous substitutions. As a substantial application example, we give the first semantic interpretation of Miller-Tiu's FOλ(nabla) logic. FOλ(nabla) logic is designed for reasoning about operational semantics of languages with binding. On the operational level, a contribution of the thesis is to extend an automata-based model for a variety of name-passing calculi with their associated notion of equivalence. HD-automata, a syntax-independent operational model, has been successfully applied for modelling e.g. early and late bisimulation in π-calculus and hyperbisimulation in Fusion calculus. However, current HD-automata are not adequate for modelling open bisimulation because they can not handle distinction-preserving substitutions. We solve this technical problem by integrating the notion of distinction into the definition of named sets, the basic building blocks of HD-automata. Finally, we discuss the relationship between HD-automata with distinctions, and D-LTS.

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Category theory is proving a useful tool in programming and program specification - not only as a descriptive language but as directly applicable to programming and specification tasks. Category theory achieves a level of generality of description at which computation is still possible. We show that theorems from category theory often have constructive proofs in the sense that they may be encoded as programs. In particular we look at the computation of colimits in categories showing that general theorems give rise to routines which considerably simplify the rather awkward computation of colimits. The general routines arising from categorical constructions can be used to build programs in the 'combinatorial' style of programming. We show this with an example - a program to implement the semantics of a specification language. More importantly, the intimate relationship between these routines and algebraic specifications allows us to develop programs from certain forms of specifications. Later we turn to algebraic specifications themselves and look at properties of "monadic theories". We establish that, under suitable conditions: 1. Signatures and presentations may be defined for monadic theories and free theories on a signature may be constructed. 2. Theory morphisms give rise to ad junctions between categories of algebras and moreover a collection of algebras of a theory give rise to a new theory with certain properties. 3. Finite colimits and certain factorisations exist in categories of monadic theories. 4. Many-sorted, order-sorted and even category-sorted theories may be handled by somewhat extending the notion of monadic theories. These results show that monadic theories are sufficiently well-behaved to be used in the semantics of algebraic specification languages. Some of the constructions can be encoded as programs by the techniques mentioned above.

Research Doctorate - Doctor of Philosophy (PhD) / It is difficult to decide when to replace (major components of) information systems (IS) used in large organisations. Obstacles include not only the cost and the technical complexities but also the fact that the workplace is dependent on the current IS and the users have familiarity with their functionalities. The problems become more complicated with increasing need for IS interconnectivity within and between organisations. Formal guidelines to assist in making replacement decisions are not commonly used. This thesis aims to develop a model of key factors involved in the IS replacement decision and to investigate the role of interoperability in this decision. It concentrates on the healthcare domain in NSW, Australia, which represents a complex distributed multilevel organisation, which has identified interoperability as a problem and has started initiatives to improve it. Research in IS and software engineering has shed light on many of the issues associated with the replacement decision. For example, studies in technology acceptance have explained why organisations delay in moving to new technologies, and modelled the effect of increasing popularity of such technologies. IS success models have explored the factors that contribute to success and failure of deployed systems, providing checklists to assess the appropriateness of current systems from the point of view of the users and other organisational stakeholders. Research into the value of user feedback has helped managers to align user expectations with workplace IS. In terms of software function, metrics have been developed to measure a range of factors including performance, usability, efficiency and reliability that help determine how well the systems are performing from a technical perspective. Additional research has identified important points to consider when comparing custom made systems versus buying off-the-shelf systems, such as skill availability and after sale support. Maturity models and life cycle analyses consider the effect of age on IS, and Lehman’s laws of software evolution highlight the need for maintenance if an IS is to survive. Improvements in interoperability at the information level have been achieved through domain specific standards for data integrity, and modular approaches for partial changes in IS. In particular, the healthcare domain has developed a number of standardised terminological systems such as SNOMED, LOINC, ICD and messaging standards such as HL7. Template high level data models have also been trialled as a way to ensure new IS remain compatible with existing systems. While this literature partially covers and contributes to the understanding of when and how to replace IS and/or components, to our knowledge there has been no attempt to provide an integrated model identifying factors to be considered in the replacement decision. The thesis adopts a multi method approach to build a model of IS replacement and to explore aspects of interoperability. Preliminary factors and their potential interactions were first identified from the literature. In depth interviews were conducted with 10 experts and 2 IS users to investigate the validity and importance of the factors and interactions and to elicit further potential items. The analysis of the transcripts guided review of further literature and contemporary data, which led to the development of a final model and insights into the role of interoperability. A member check was used to validate both the model and the researcher’s conclusions on interoperability. The final model is centred about the change request, that is, any request made by or on behalf of an executive officer in order to maintain or replace part or all of an IS. The change request is informed by user feedback but our research distinguishes the two factors because the change request factor filters and manages requests for change from multiple sources. Other factors that have an important direct or indirect effect on generating change requests include: the extent of system specialisation, that is, how the system is tailored to satisfy organisational requirements; popularity, the degree to which an IS or a component is liked or supported by its user community; the prevalence and severity of errors and failures in the systems; the usability and performance of the systems; and the adequacy of support, including training, documentation, and so on. The dependent factors are maintenance and replacement, determined through the change requests. The validation through member checking showed that IS practitioners found our model useful in explaining the replacement process. The model provided an interpretation of the change requests. By exposing and clustering reasons behind the change requests, the complexity of deciding whether to maintain or replace system components can be reduced. Individual factors can be addressed more specifically. Formal guidelines on whether to maintain or replace components or entire IS can be drawn up using this understanding. The factors and their interactions as explained in the model could be the basis of a decision tree, which would be customised for organisational jargon and priorities. The requirement for interoperability is an aspect of system specialisation. An important finding from the research was that one of the most significant reasons to change a system is when problems are encountered in exchanging data and information. Conversely, as long as systems can exchange data, there is less pressure to replace them. Organisations benefit more from systems that provide more support for interoperability. Findings on interoperability in the health domain were that existing messaging standards (mostly HL7) used in the information exchange between subsystems including legacy databases are useful and are used. Also, ambiguities are diminished with vocabularies (mostly SNOMED, LOINC and ICD are used in NSW health domain). However, a methodology known as Interoperability Framework supported by government funding bodies for comparing data models has not been adopted and is not given any significant credit by the users. Likewise, a government proposal to use an overarching high level data model has not been adopted, in part because it is too complex. To guide use of such a data model requires a methodology for comparing data models: an example of such a methodology is developed in this thesis. The thesis research found that replacement decisions in the healthcare domain are affected by the existing quasi-monopoly of large vendors which tend to use proprietary standards that limit interoperability. The research concludes that interoperability should be achieved by increased use of vendor-independent messaging and terminological standards. In order to get the co-operation of individual health institutions within the domain, initial investments should be concentrated on simple and easy to adopt standards. A primary limitation of this thesis is the extent of testing of the findings. Data from a broader range of organisations, in different sectors and different countries, is needed to validate the model and to guide development of decision making tools that are based on it. Particularly valuable would be case studies of IS replacement decision making and the process which executives use in determining change requests. The priorities of the factors and their attributes as well as the strengths of the relationships in the model need to be tested empirically using tailored survey instruments. Another interesting research avenue which was only touched on in the thesis was the effect of policies and legislation on interoperability and on replacement decisions.

In thinking about quantum causality one would like to approach rigorous QFT from outside the perspective of QFT, which one expects to recover only in a specific physical domain of quantum gravity. This thesis considers issues in causality using Category Theory, and their application to field theoretic observables. It appears that an abstract categorical Machian principle of duality for a ribbon graph calculus has the potential to incorporate the recent calculation of particle rest masses by Brannen, as well as the Bilson-Thompson characterisation of the particles of the Standard Model. This thesis shows how Veneziano n point functions may be recovered in such a framework, using cohomological techniques inspired by twistor theory and recent MHV techniques. This distinct approach fits into a rich framework of higher operads, leaving room for a generalisation to other physical amplitudes. The utility of operads raises the question of a categorical description for the underlying physical logic. We need to consider quantum analogues of a topos. Grothendieck's concept of a topos is a genuine extension of the notion of a space that incorporates a logic internal to itself. Conventional quantum logic has yet to be put into a form of equal utility, although its logic has been formulated in category theoretic terms. Axioms for a quantum topos are given in this thesis, in terms of braided monoidal categories. The associated logic is analysed and, in particular, elements of linear vector space logic are shown to be recovered. The usefulness of doing so for ordinary quantum computation was made apparent recently by Coecke et al. Vector spaces underly every notion of algebra, and a new perspective on it is therefore useful. The concept of state vector is also readdressed in the language of tricategories.

Codensity monads are ubiquitous, as are various different notions of compactness and finiteness. Two such examples of "compact" spaces are compact Hausdorff Spaces and Linearly Compact Vector Spaces. Compact Hausdorff Spaces are the algebras of the codensity monad induced by the inclusion of finite sets in the category of sets. Similarly linearly compact vector spaces are the algebras of the codensity monad induced by the inclusion of finite dimensional vector spaces in the category of vector spaces. So in these two examples the notions of finiteness, compactness and codensity are intertwined. In this thesis we generalise these results. To do this we generalise the notion of ultrafilter, and follow the intuition of the compact Hausdorff case. We give definitions of general notions of "finiteness" and "compactness" and show that the algebras for the codensity monad induced by the "finite" objects are exactly the "compact" objects.

In this thesis, tools of categorical quantum mechanics are used to explain natural language from a cognitive point of view. Categories of generalized relations are developed for the task, examples are provided, and languages that are particularly tricky to describe using this approach are taken into consideration.

The main goal of this thesis is to construct a tensor product on the 2-category BFC-A of braided fusion categories containing a symmetric fusion category A. We achieve this by introducing the new notion of Z(A)-crossed braided categories. These are categories enriched over the Drinfeld centre Z(A) of the symmetric fusion category. We show that Z(A) admits an additional symmetric tensor structure, which makes it into a 2-fold monoidal category. ByTannaka duality, A= Rep(G) (or Rep(G; w)) for a finite group G (or finite super-group (G,w)). Under this identication Z(A) = VectG[G], the category of G-equivariant vector bundles over G, and we show that the symmetric tensor product corresponds to (a super version of) to the brewise tensor product. We use the additional symmetric tensor product on Z(A) to define the composition in Z(A)-crossed braided categories, whereas the usual tensor product is used for the monoidal structure. We further require this monoidal structure to be braided for the switch map that uses the braiding in Z(A). We show that the 2-category Z(A)-XBF is equivalent to both BFC=A and the 2-category of (super)-G-crossed braided categories. Using the former equivalence, the reduced tensor product on BFC-A is dened in terms of the enriched Cartesian product of Z(A)-enriched categories on Z(A)-XBF. The reduced tensor product obtained in this way has as unit Z(A). It induces a pairing between minimal modular extensions of categories having A as their Mueger centre.

Este trabalho propõe o estudo dos espaços coerentes do ponto de vista da teoria dos topos, ou seja, consiste em uma análise, em termos de topos, das principais categorias de espaços coerentes. Os espaços coerentes constituem um tipo de domínio que apresenta algumas particularidades que o distinguem dos demais, por exemplo, considera admissíveis no conjunto de funções somente aquelas que, além de contínuas no sentido de Scott - preservam supremos de conjuntos dirigidos, também são estáveis e lineares. Um topos e uma categoria Cartesiana fechada com classificador de subobjetos. Isso faz com que todo topos se comporte como Set (conjuntos como objetos e funções como morfismos), ou seja, uma categoria na qual as interpretações de suas construções básicas seguem a Teoria dos Conjuntos. Entre as categorias de Espaços Coerentes, tem-se a categoria STAB, cujos objetos são os espaços coerentes e os morfismos são funções estáveis entre esses espaços, que é uma categoria cartesiana fechada. Isto significa que STAB é uma categoria especial no sentido computacional: além de possuir o produto binário para todos os seus objetos, STAB apresenta objeto exponencial e morfismo de avaliação, garantindo significado para processos computacionais. A subcategoria LIN da categoria STAB, cujos morfismos são as funções lineares, não é uma categoria cartesiana fechada. Entretanto, LIN é uma categoria monoidal simétrica que e fechada. Este, condição e suficiente para que em LIN também se tenha a garantia de se obter significado para processos computacionais. Apresenta-se então, uma interpretação computacional da estrutura destas categorias e uma análise das mesmas do ponto de vista de topos, isto é, da existência ou não de classificador de subobjetos. / This work proposes the study of coherent spaces from the point of view of the Topos Theory, that is, it consists of an analysis of the main categories of coherent spaces in terms of topos. The coherent spaces make up a kind of domain which presents some peculiarities that separate it from the rest, for example, in the complex whole of the functions it only considers permissible, those which, apart from being continuous in the sense of Scott - preserving supremo of directed sets, it is also stable and linear. A topos is a Cartesian closed with subobject classifier. This makes topos behaves like Set (sets as objects and functions as morphisms), that is, a category in which the interpretations of its basic constructions follow the Theory of Sets. Among the categories of Coherent Spaces, there is the STAB category, a closed Cartesian category, the objects of which are the coherent spaces, having morphisms as stable functions among these spaces. This means that STAB is a special category in the computational sense: apart from having a binary product for all its objects, STAB presents an exponential object and a morphism of evaluation, ensuring meaning for computational processes. The subcategory LIN of the STAB category, the morphisms of which are linear functions, is not a closed Cartesian category. However, LIN is a symmetrical monoidal category which is closed. This condition is sufficient to also have in LIN the guarantee of obtaining meaning for computational processes. Thus, a computational interpretation of the structure of these categories will be presented, as well as an analysis of them from the point of view of the Topos Theory, that is, if subobject classifier exists or not.

Este trabalho propõe o estudo dos espaços coerentes do ponto de vista da teoria dos topos, ou seja, consiste em uma análise, em termos de topos, das principais categorias de espaços coerentes. Os espaços coerentes constituem um tipo de domínio que apresenta algumas particularidades que o distinguem dos demais, por exemplo, considera admissíveis no conjunto de funções somente aquelas que, além de contínuas no sentido de Scott - preservam supremos de conjuntos dirigidos, também são estáveis e lineares. Um topos e uma categoria Cartesiana fechada com classificador de subobjetos. Isso faz com que todo topos se comporte como Set (conjuntos como objetos e funções como morfismos), ou seja, uma categoria na qual as interpretações de suas construções básicas seguem a Teoria dos Conjuntos. Entre as categorias de Espaços Coerentes, tem-se a categoria STAB, cujos objetos são os espaços coerentes e os morfismos são funções estáveis entre esses espaços, que é uma categoria cartesiana fechada. Isto significa que STAB é uma categoria especial no sentido computacional: além de possuir o produto binário para todos os seus objetos, STAB apresenta objeto exponencial e morfismo de avaliação, garantindo significado para processos computacionais. A subcategoria LIN da categoria STAB, cujos morfismos são as funções lineares, não é uma categoria cartesiana fechada. Entretanto, LIN é uma categoria monoidal simétrica que e fechada. Este, condição e suficiente para que em LIN também se tenha a garantia de se obter significado para processos computacionais. Apresenta-se então, uma interpretação computacional da estrutura destas categorias e uma análise das mesmas do ponto de vista de topos, isto é, da existência ou não de classificador de subobjetos. / This work proposes the study of coherent spaces from the point of view of the Topos Theory, that is, it consists of an analysis of the main categories of coherent spaces in terms of topos. The coherent spaces make up a kind of domain which presents some peculiarities that separate it from the rest, for example, in the complex whole of the functions it only considers permissible, those which, apart from being continuous in the sense of Scott - preserving supremo of directed sets, it is also stable and linear. A topos is a Cartesian closed with subobject classifier. This makes topos behaves like Set (sets as objects and functions as morphisms), that is, a category in which the interpretations of its basic constructions follow the Theory of Sets. Among the categories of Coherent Spaces, there is the STAB category, a closed Cartesian category, the objects of which are the coherent spaces, having morphisms as stable functions among these spaces. This means that STAB is a special category in the computational sense: apart from having a binary product for all its objects, STAB presents an exponential object and a morphism of evaluation, ensuring meaning for computational processes. The subcategory LIN of the STAB category, the morphisms of which are linear functions, is not a closed Cartesian category. However, LIN is a symmetrical monoidal category which is closed. This condition is sufficient to also have in LIN the guarantee of obtaining meaning for computational processes. Thus, a computational interpretation of the structure of these categories will be presented, as well as an analysis of them from the point of view of the Topos Theory, that is, if subobject classifier exists or not.