The Canonical Grothendieck Topology and a Homotopical Analog
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Date
2019-09-18
Authors
Lester, Cynthia
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
We explore the canonical Grothendieck topology and a new homotopical analog. First we discuss a specific description of the covers in the canonical topology, which we then use to get a corollary of Giraud's Theorem. Second we delve into the canonical topology on some specific categories, e.g. on the category of topological spaces and the category of abelian groups; this part includes concrete examples and non-examples. Lastly, we discuss a homotopical analog of the canonical Grothendieck topology
and explore some examples of this analog.
Description
Keywords
colim sieve, effective epimorphism, generalized sieve, hocolim sieve, homotopical canonical topology, index-functor category