# nLab Segal's category

Contents

This entry is about the small category named after Graeme Segal. Not to be confused with the model in higher category theory called Segal categories.

# Contents

## Definition

###### Definition

Segal’s category, denoted $\Gamma$ is the category opposite to the skeleton of the category $FinSet^{*/}$ of pointed finite sets:

$\Gamma^{op} \simeq FinSet^{*/} \,.$
###### Remark

The category $\Gamma$ is related to (infinity,1)-operads in a way similar to how the simplex category (non-empty and linearly ordered finite sets) is related to (∞,1)-categories.

###### Remark

A morphism $f \colon \{*\} \coprod S \to \{*\} \coprod T$ in $\Gamma$ may be thought of as a partially defined function $\tilde f \colon S \to T$ which is undefined on all elements of $S$ that $f$ sends to the point.

## References

For instance notation 2.0.0.2 in

Last revised on December 3, 2014 at 03:24:30. See the history of this page for a list of all contributions to it.