# nLab pentagon identity

Contents

### Context

#### Monoidal categories

monoidal categories

# 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

$a_{x,y,z} \;\colon\; (x \otimes y) \otimes z \longrightarrow x \otimes (y \otimes z)$

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.