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
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.