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
Definitions
Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
Compact bicategories are bicategory in which every 1-morphisms has a left adjoint and a right adjoint. These are the horizontal categorification of rigid monoidal categories, i.e. of non-symmetric compact closed categories.
This should be distinguished from compact closed bicategories, which are monoidal bicategories with duals, i.e. the vertical categorification of compact closed categories.
Ross Street, Bob Walters, Yoneda structures on 2-categories, JPAA 50 (1978) 350-379 [doi:10.1016/0021-8693(78)90160-6]
Anne Preller?, Joachim Lambek, Free Compact 2-Categories, Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2007 (pdf)
Last revised on April 20, 2024 at 15:24:06. See the history of this page for a list of all contributions to it.