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
A category is bicartesian if it is both cartesian and cocartesian, that is if both it and its opposite may be made into cartesian monoidal categories. Note this is different than a semiadditive category, i.e. a category with coinciding products and coproducts. Thus every semiadditive category is bicartesian, but not every bicartesian category is semiadditive.
A bicartesian category which is also cartesian closed is a bicartesian closed category. Bicartesian closed categories are usually not cocartesian closed.
Last revised on April 11, 2025 at 08:24:12. See the history of this page for a list of all contributions to it.