Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/90348
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- Title
- The Comprehensive factorisation and torsors
- Related
- Theory and applications of categories, Vol. 23, No. 3 (2010), p.42-75
- Related
- http://www.tac.mta.ca/tac/volumes/23/3/23-03.pdf
- Publisher
- Mount Allison University, Department of Mathematics and Science
- Date
- 2010
- FoR/RFCD Code(s)
-
010103 Category Theory, K Theory, Homological Algebra
- Author/Creator
- Street, Ross
- Author/Creator
- Verity, Dominic
- Description
- This is an expanded, revised and corrected version of the first author's 1981 preprint. The discussion of one-dimensional cohomology H¹ in a fairly general category ℇ involves passing to the 2-category Cat(ℇ) of categories ℇ. In particular, the coefficient object is a category B in ℇ and the torsors that H¹ classifies are particular functors in ℇ. We only impose conditions on ℇ that are satisfied also by Cat(ℇ) and argue that H¹ for Cat(ℇ) is a kind of H² for ℇ, and so on recursively. For us, it is too much to ask ℇ to be a topos (or even internally complete) since, even if ℇ is, Cat(ℇ) is not. With this motivation, we are led to examine morphisms in ℇ which act as internal families and to internalize the comprehensive factorization of functors into a final functor followed by a discrete fibration. We define B-torsors for a category Β in ℇ and prove clutching and classification theorems. The former theorem clutches Čech cocycles to construct torsors while the latter constructs a coefficient category to classify structures locally isomorphic to members of a given internal family of structures. We conclude with applications to examples.
- Description
- 34 page(s)
- Subject Keyword
- 010103 Category Theory, K Theory, Homological Algebra
- Subject Keyword
- torsor
- Subject Keyword
- internal category
- Subject Keyword
- exponentiable morphism
- Subject Keyword
- discrete fibration
- Subject Keyword
- final functor
- Subject Keyword
- comprehensive factorization
- Subject Keyword
- locally isomorphic
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Computing
- Identifier
- http://hdl.handle.net/1959.14/90348
- Identifier
- ISSN:1201-561X
- Identifier
- mq-rm-2009006102
- Language
- eng
- Reviewed
