With duals for objects
With duals for morphisms
Special sorts of products
In higher category theory
A bipermuatative category is a permutative category with a second symmetric monoidal category structure that distributes over , with, again, some of the coherence laws required to hold strictly.
(May, def. VI 3.3) (Elmendorf-Mandell, def. 3.6)
Relation to bimonoidal categories
Every symmetric bimonoidal category is equivalent to a bipermutative category (May, prop. VI 3.5).
- Peter May, Ring Spaces and Ring spectra, Springer lectures notes in mathematics, Vol. 533, (1977) (pdf) chaper VI
Revised on October 8, 2012 15:18:04
by Urs Schreiber