Profinite Cosheaves Valued in Pro-regular Categories
Jiacheng Tang

TL;DR
This paper demonstrates that the category of profinite cosheaves valued in a pro-regular category is itself pro-regular, extending existing equivalences to profinite groups.
Contribution
It establishes the pro-regularity of profinite cosheaves valued in pro-regular categories and extends cosheaf-bundle equivalence to profinite groups.
Findings
Category of profinite cosheaves is pro-regular
Extended cosheaf-bundle equivalence to profinite groups
Generalized Wilkes's equivalence
Abstract
We prove that the category of profinite cosheaves valued in a pro-regular category (satisfying mild assumptions) is itself a pro-regular category. As a corollary, we extend Wilkes's cosheaf-bundle equivalence from profinite modules to profinite groups.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Rings, Modules, and Algebras
