Sheaves on T-topologies

TL;DR

This paper introduces T-topologies as a unifying framework for various geometric and topological constructions, and studies the associated category of T-sheaves.

Contribution

It provides a unified approach to subanalytic, semialgebraic, and o-minimal sites through T-topologies, expanding the understanding of sheaf categories.

Findings

Unified description of different sites via T-topologies

Analysis of the category of T-sheaves

Potential applications to geometric and topological theories

Abstract

The aim of this paper is to give a unifying description of various constructions (subanalytic, semialgebraic, o-minimal site) using the notion of T-topology. We then study the category of T-sheaves.