# nLab reverse category

### Context

#### Monoidal categories

monoidal categories

# Contents

## Definition

The reverse category of a monoidal category, $\mathcal{C}$, has the same underlying category and unit as $\mathcal{C}$ but reversed monoidal product, $X \otimes^{rev} Y = Y \otimes X$, and similarly for morphisms. The associator in the reverse category is $\alpha^{rev}_{X,Y,Z} = \alpha^{-1}_{Z,Y,X}$.