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.

Contents

Definition

Definition

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

Γ opFinSet */. \Gamma^{op} \simeq FinSet^{*/} \,.
Remark

The category Γ\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:{*}S{*}Tf \colon \{*\} \coprod S \to \{*\} \coprod T in Γ\Gamma may be thought of as a partially defined function f˜:ST\tilde f \colon S \to T which is undefined on all elements of SS that ff 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.