category theory

# Contents

## Definition

A category is called gaunt if all its isomorphisms are in fact identities. This is really a property of strict categories; that is, it is not invariant under equivalence of categories.

## Properties

### Relation to complete Segal spaces

The nerve simplicial set of a category, regarded as a simplicial object in homotopy types under the inclusion $Set \hookrightarrow \infty Grpd$, is a complete Segal space precisely if the category is gaunt. More discussion of this is at Segal space – Examples – In Set.

## References

The term “gaunt category” was apparently introduced in

in the context of a discussion of (infinity,n)-categories.

Revised on November 30, 2012 02:09:19 by Toby Bartels (64.89.53.239)