nLab pentagon identity

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).

Related concepts

• coherence law

• pentagonator

References

• André Joyal,Ross Street, p. 10 of Braided tensor categories, Adv. Math. 1993 (pdf)

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