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 November 27, 2023 at 09:44:41. See the history of this page for a list of all contributions to it.