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
Definitions
Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
A probicategory is a “many-object” generalisation of a promonoidal category, in the same way that a bicategory is a “many-object” generalisation of a monoidal category.
Just as a promonoidal category in the most general context in which we can perform Day convolution to obtain a monoidal structure on the category of presheaves, a probicategory is the most general context in which we can perform convolution locally to obtain a bicategory structure on the local cocompletion.
A probicategory is a bicategory enriched in the monoidal bicategory Prof.
Given a probicategory, we may form a bicategory by change of base along the pseudofunctor from Prof to Cat given by taking free cocompletion. When applied to a one-object probicategory (i.e. a promonoidal category), this produces the (monoidal) presheaf category obtained through Day convolution.
A summary of the results of the thesis may be found in:
Created on September 7, 2024 at 10:34:44. See the history of this page for a list of all contributions to it.