# nLab bipermutative category

### Context

#### Monoidal categories

monoidal categories

## With traces

• trace

• traced monoidal category?

# Contents

## Idea

A bipermuatative category is a permutative category $\left(C,\oplus \right)$ with a second symmetric monoidal category structure $\left(C,\otimes \right)$ that distributes over $\oplus$, with, again, some of the coherence laws required to hold strictly.

## Properties

### Relation to bimonoidal categories

Every symmetric bimonoidal category is equivalent to a bipermutative category (May, prop. VI 3.5).

## References

• Peter May, ${E}_{\infty }$ Ring Spaces and ${E}_{\infty }$ Ring spectra, Springer lectures notes in mathematics, Vol. 533, (1977) (pdf) chaper VI

Revised on October 8, 2012 15:18:04 by Urs Schreiber (82.169.65.155)