# nLab microflexible sheaf

Contents

## Theorems

#### $(\infty,1)$-Topos Theory

(∞,1)-topos theory

## Constructions

structures in a cohesive (∞,1)-topos

# Contents

## Definition

Denote by $Emb_n$ the site of $n$-dimensional smooth manifolds and open embeddings.

An (∞,1)-sheaf $F\colon Emb_n^op\to Top$ of topological spaces is microflexible if for any closed inclusion $K\to K'$ of compact spaces, the induced map $F(K')\to F(K)$ is a Serre microfibration.

An (∞,1)-sheaf $F\colon Emb_n^op\to Top$ of topological spaces is flexible if for any closed inclusion $K\to K'$ of compact spaces, the induced map $F(K')\to F(K)$ is a Serre fibration.

## Gromov’s theorem

Given an open manifold $M$, the inclusion of microflexible sheaves into flexible sheaves on the slice site site $Emb_n/M$ is an equivalence of (∞,1)-categories.

## Literature

The original reference is

• M. L. Gromov?, Stable mappings of foliations into manifolds, Mathematics of the USSR-Izvestiya 3:4 (1969), 671-694. doi.

The canonical reference is Section 2.2.1 of

See also

Last revised on May 9, 2022 at 13:00:33. See the history of this page for a list of all contributions to it.