With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
monoidal dagger-category?
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
For a functor between categories that are equipped with the structure of monoidal categories , , a lax monoidal structure map is a natural transformation
that equips with the structure of a lax monoidal functor.
Similarly, an oplax monoidal structure map, or lax comonoidal structure map is a natural transformation
that equips with the structure of an oplax monoidal functor.
An (op)lax (co)monoidal structure map is sometimes called an (op)lax (co)monoidal transformation; however, this is not a laxification (a directed weakening) of any strong notion of monoidal natural transformation (which has nothing to laxify).
Last revised on September 7, 2011 at 16:34:06. See the history of this page for a list of all contributions to it.