An internal description of constructible objects in an $\infty$-topos

TL;DR

This paper provides an internal framework for understanding constructible objects within an $$-topos, characterizing them as locally constant objects in a functor category related to noetherian posets.

Contribution

It introduces an internal description of constructible objects in an $$-topos, linking them to locally constant objects in a functor category for any noetherian poset.

Findings

Constructible objects are characterized internally as locally constant objects.

The description applies to any noetherian poset.

Provides a new perspective on the internal structure of constructible objects.

Abstract

We give an internal description of constructible objects in an $\infty$-topos. More precisely, $P$-consctructible objects are locally constant objects internal to Fun($P$,An), for any noetherian poset $P$.