nLab Segal's category

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.

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.

Related concepts

• Gamma space

References

For instance notation 2.0.0.2 in

• Jacob Lurie, Higher Algebra