Profinite Cosheaves Valued in Pro-regular Categories

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.