gaunt category

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.

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*.

The term “gaunt category” was apparently introduced in

- Clark Barwick, Chris Schommer-Pries,
*On the Unicity of the Homotopy Theory of Higher Categories*(arXiv:1112.0040, slides)

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

Last revised on November 30, 2012 at 02:09:19. See the history of this page for a list of all contributions to it.