In the paper \cite{FHS12}, the authors announce the discovery of an invariant for Grothendieck toposes which they call the isotropy group of a topos. Roughly speaking, the isotropy group of a topos carries algebraic data in a way reminiscent of how the subobject classifier carries spatial data. Much as we like to compute invariants of spaces in algebraic topology, we would like to have tools to calculate invariants of toposes in category theory. More precisely, we wish to be in possession of theorems which tell us how to go about computing (higher) isotropy groups of various toposes. As it turns out, computation of isotropy groups in toposes can often be reduced to questions at the level of small categories and it is therefore interesting to try and see how isotropy behaves with respect to standard constructions on categories. We aim to provide a summary of progress made towards this goal, including results on various commutation properties of higher isotropy quotients with colimits and the way isotropy quotients interact with categories collaged together via certain nice kinds of profunctors. The latter should be thought of as an analogy for the Seifert-van Kampen theorem, which allows computation of fundamental groups of spaces in terms of fundamental groups of smaller subspaces.

Category management (CM) is an approach of cooperation on category development between supplier and retailer. Supplier brings the knowledge of consumer and products within the category. Retailer brings sell-out data. The whole concept is based on managing categories as strategic business units and delivering maximum value to consumer in form of satisfying his needs. Even though first CM projects in ČR started about 15 years ago, most of the companies have not been able to fully implement CM. The barriers are high organizational demands on integration of CM into company structure and the necessity of trust between the supplier and the retailer in form of sharing data. The objective of this thesis is to identify opportunities in CM based on the analysis of current business process in Plzeňský Prazdroj, a. s. Opportunities identification is reached through comparison of ideal business process defined by specialized literature with the real experience from Plzeňský Prazdroj. Opportunities to enhance the current setting of the CM process will be summarized based on the comparison. Also, new areas of possible utilization of CM will be pointed out.

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Background: Patients with mental illness often experience stigma and marginalization, which affects the quality of their healthcare. In most settings, end of life decisions, including goals of care, must be discussed with all patients upon hospital admission. This includes determining cardiopulmonary resuscitation preferences, in the event of a medical emergency. Despite this requirement, category status conversations do not routinely occur in psychiatry. It is common for psychiatric inpatients, including those at high risk for cardiac or respiratory arrest, to be admitted, cared for, and discharged without their category status known or documented. By default, patients become a ‘full code status’, which mandates life-sustaining interventions, including CPR. Unwanted interventions are often unsuccessful and inappropriate. They might also cause harm through increased pain and suffering or have no medical benefit. Aim: To explore how and why category status conversations occur, or do not occur, for patients admitted to psychiatry. Methods: This was a descriptive qualitative study, with data collected through two semi-structured focus groups. Nine nurses working in psychiatry, representing two campuses of a larger tertiary care academic hospital in Ottawa, Ontario participated. Elo and Kyngäs’s approach to inductive content analysis was used to analyze the verbatim transcripts of the focus group discussions. Findings: Findings reveal the shared experiences of nurses initiating and engaging in category status conversations with patients admitted to psychiatry. Four overarching categories were identified: ‘The Psychiatric Culture’, ‘Being a Psychiatric Patient’, ‘Physical Health Status’, and ‘Suggestions and Recommendations’. Participants spoke about important considerations for the advancement of knowledge regarding category status conversations in psychiatry, including the nurse’s role in category status determination, the challenges of implementing a ‘one-size fits all’ approach to category status policies, and the ways in which HCPs perceptions of patients who are receiving care for depression or suicidal ideation influence these conversations in psychiatry. Conclusion: Nurses working in psychiatry care for patients with complex medical and psychiatric comorbidities, who are also sometimes older and frail. Category status determination for these patients is complicated and often the documented status is based on clinician presumption rather than consultation with the patient. Although the importance of completing category status conversations with patients admitted to psychiatry is known, they seldomly occur, and there is ambiguity about the nursing role within the psychiatric context. Efforts are needed to improve nurses’ contributions to category status determination for patients admitted to psychiatry, to ensure that patients’ preferences are known and upheld. Further, there are illness-related factors that complicate typical processes used to discuss and identify patient preferences, such as suicidal ideation and minimal family support. These considerations must be accounted for in hospital policy if meaningful practice change is expected.

In the past decade, the COVIS model (Ashby, Alfonso-Reese, Turken, & Waldron, 1998) has emerged as the only neuropsychological theory for the existence of multiple brain systems for category learning. COVIS postulates that there are two systems, explicit and implicit, which compete against one another. These two systems reply on two discrete networks: explicit, or rule based categorization relies on executive function and working memory while implicit, or information integration categorization is mediated by dopaminergic pathways. The purpose of this pilot study was to further provide evidence for the existence of multiple systems of category learning. In all three experiments, we interrupted feedback processing using a modified Sternberg task. In Experiment 1 and 2, participants were separated into four conditions, rule based (RB) categorization with a short delay between feedback and the modified Sternberg task, RB categorization with a long delay, information integration (II) categorization with a short delay, and II categorization with a long delay. Participants in the RB conditions performed worse than those in the II conditions in Experiment 1 and 2. After determining there was no significant difference between the short and long delay manipulations, only the short delay was used for Experiment 3. Consistent with Experiment 1 and 2, participants in the RB condition performed worse than those in the II condition. Functional near-infrared spectroscopy (fNIRS) technology was also used in Experiment 3 to determine the difference in prefrontal activation between RB and II conditions. Although statistically not significant, across blocks, the difference in prefrontal activation increased.

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This thesis deals with generalized fibre spaces. It improves upon existing definitions and introduces new ones. It establishes the category of pairs and the category of g.f.s. The relationship between classical fibre spaces and generalized fibre spaces is examined. The induced g.f.s. is defined as well as the concept of section and it is established that the lifting of a fully regular continuous g-function is equivalent to the existence of a section in the induced g.f.s. Finally the lifting theorem for g.f.s. is stated and proved. / Thesis / Doctor of Philosophy (PhD)

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