On the homological dimension of o-minimal and subanalytic sheaves

TL;DR

This paper establishes finite bounds on the homological dimension of sheaves in o-minimal and subanalytic contexts, providing new insights into their algebraic and topological properties.

Contribution

It introduces conditions under which the homological dimension of sheaves in o-minimal and subanalytic settings is finite, advancing understanding of their structural complexity.

Findings

Homological dimension of sheaves is finite under certain conditions

Boundaries for homological dimension in o-minimal sheaves established

Boundaries for homological dimension in subanalytic sheaves established

Abstract

Here we prove that the homological dimension of the category of sheaves on a topological space satisfying some suitable conditions is finite. In particular, we find conditions to bound the homological dimension of o-minimal and subanalytic sheaves.