Thesis (Ph. D.)--University of Oregon, 1999. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 103-105). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9947969.

Typescript. Includes vita and abstract. Includes bibliographical references (leaves 53-54) Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

Thesis (doctoral)--Universidad de Santiago de Compostela, 1981. / Bibliography: p. 150-158.

We introduce the notion of cellular dg-categories mimicking the properties of topological CW-complexes. We study the properties of such categories and provide various examples corresponding to the well-known geometrical objects. We also show that these categories are suitable for encoding coherence conditions in homotopy theoretical constructs involving A-infinity categories. In particular, we formulate the notion of a homotopy coherent monoid action on an A-infinity category which can be used in constructions involved in Homological Mirror Symmetry.

<p>Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological stability for the homology of the unordered configuration spaces of a connected manifold. The main difficulty is the case that the manifold is compact because there are no obvious maps inducing stability and the homology eventually is periodic instead of stable. We resolve this issue by constructing a new chain-level stabilization map for configuration spaces.</p>

We study relative homological algebra and relative Hochschild cohomology. We dualise the construction in [Cib+21b] for a ring extension B ⊆ A to construct a long nearly exact sequence for the relative Hochschild cohomology HH∗(A|B), the Hochschild cohomology HH∗(A) and the Hochschild cohomology HH∗(B,A). Parallel to this we also study corings and the associated Cartier cohomology and Hochschild cohomology. Given an A-coring C and its right algebra R we have induced maps ExtiA(M, N) → ExtiR(R⊗A M, R⊗A N) by the induction functor. We characterise the vanishing of the Hochschild cohomology of the coring in terms of these induced maps being isomorphisms for degrees greater than or equal to one.

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Some of the diagram lemmas of Homological Algebra, classically known for abelian categories, are not characteristic of the abelian context; this naturally leads to investigations of those non-abelian categories in which these diagram lemmas may hold. In this Thesis we attempt to bring together two different directions of such investigations; in particular, we unify the five lemma from the context of homological categories due to F. Borceux and D. Bourn, and the five lemma from the context of modular semi-exact categories in the sense of M. Grandis. / AFRIKAANSE OPSOMMING: Verskeie diagram lemmata van Homologiese Algebra is aanvanklik ontwikkel in die konteks van abelse kategorieë, maar geld meer algemeen as dit behoorlik geformuleer word. Dit lei op ’n natuurlike wyse na ’n ondersoek van ander kategorieë waar hierdie lemmas ook geld. In hierdie tesis bring ons twee moontlike rigtings van ondersoek saam. Dit maak dit vir ons moontlik om die vyf-lemma in die konteks van homologiese kategoieë, deur F. Borceux en D. Bourn, en vyflemma in die konteks van semi-eksakte kategorieë, in die sin van M. Grandis, te verenig.

An integral domain D is weakly integrally closed if whenever there is an element x in the quotient field of D and a nonzero finitely generated ideal J of D such that xJ J2, then x is in D. We define weakly integrally closed numerical monoids similarly. If a monoid algebra is weakly integrally closed, then so is the monoid. A pattern F of finitely many 0's and 1's is forbidden if whenever the characteristic binary string of a numerical monoid M contains F, then M is not weakly integrally closed. Any stretch of the pattern 11011 is forbidden. A numerical monoid M is weakly integrally closed if and only if it has a forbidden pattern. For every finite set S of forbidden patterns, there exists a monoid that is not weakly integrally closed and that contains no stretch of a pattern in S. It is shown that particular monoid algebras are weakly integrally closed. / by Mary E. Hopkins. / Thesis (Ph.D.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

Neste trabalho, estudamos a cohomologia de de Rham e métodos para os seus cálculos. Finalizamos com aplicações da cohomologia de de Rham em teoremas da topologia / In this work we study the de Rham cohomology and methods for its calculations. We close it with applications of the Rham cohomology in theorems from topology

This thesis consists of three papers about N-complexes and their uses in categorification. N-complexes are generalizations of chain complexes having a differential d satisfying dN = 0 rather than d2 = 0. Categorification is the process of finding a higher category analog of a given mathematical structure. Paper I: We study a set of homology functors indexed by positive integers a and b and their corresponding derived categories. We show that there is an optimal subcategory in the domain of every functor given by N-complexes with N = a + b. Paper II: In this paper we show that the lax nerve of the category of chain complexes is pointwise adjoint equivalent to the décalage of the simplicial category of N-complexes. This reveals additional simplicial structure on the lax nerve of the category of chain complexes which provides a categorfication of the triangulated homotopy category of chain complexes. We study this in general and present evidence that the axioms of triangulated categories have a simplicial origin. Paper III: Let n be a product of two distinct prime numbers. We construct a triangulated monoidal category having a Grothendieck ring isomorphic to the ring of n:th cyclotomic integers.