nLab
pentagon identity

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Contents

Idea

The pentagon identity is the coherence identity satisfied by an associator in a monoidal category or more generally in a bicategory, (2,1)-category etc, asserting that the following pentagonal diagram commutes, where

a x,y,z:(xy)zx(yz) a_{x,y,z} \;\colon\; (x \otimes y) \otimes z \longrightarrow x \otimes (y \otimes z)

is the associator natural transformation (or more generally: associator 2-morphism).

References

For more references see at braided monoidal category and at coherence law.

Last revised on May 2, 2021 at 12:28:44. See the history of this page for a list of all contributions to it.