5 papers · 1 filter
Categorical Bass-Serre Theory for Tree Quotients
Jiacheng Tang
We develop a categorical framework for Bass-Serre theory, which recovers parts of classical and profinite Bass-Serre theories for tree quotients. More precisely, we show that in wh…
Profinite Cosheaves Valued in Pro-regular Categories
Jiacheng Tang
We prove that the category of profinite cosheaves valued in a pro-regular category (satisfying mild assumptions) is itself canonically a pro-completion. As a corollary, we extend W…
Profinite and Solid Cohomology
Jiacheng Tang
Solid abelian groups, as introduced by Dustin Clausen and Peter Scholze, form a subcategory of all condensed abelian groups satisfying some ''completeness'' conditions and having f…
Coproducts Internal to Profinite Spaces
Jiacheng Tang
We give a categorical explanation for many properties of profinite coproducts of profinite groups, which were previously proven on a case-by-case basis. All of these properties tak…
Open Condensed Subgroups and Mackey's Formula
Jiacheng Tang
We define what it means for a condensed group action to be open (following Scholze) and show that for open subgroups, many elementary results about abstract modules hold for conden…