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Title: Codensity, compactness and ultrafilters
Author: Devlin, Barry-Patrick
ISNI:       0000 0004 5991 8713
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2016
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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.
Supervisor: Leinster, Thomas ; Maciocia, Antony Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: category theory ; finiteness ; compactness ; Hausdorff Spaces ; Linearly Compact Vector Spaces