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7 papers · 2 filters
Tensor products of finitely cocomplete and abelian categories
Ignacio Lopez Franco
The purpose of this article is to study the existence of Deligne's tensor product of abelian categories by comparing it with the well-known ten- sor product of finitely cocomplete…
Fibred 2-categories and bicategories
Mitchell Buckley
We generalise the usual notion of fibred category; first to fibred 2-categories and then to fibred bicategories. Fibred 2-categories correspond to 2-functors from a 2-category into…
Restriction categories as enriched categories
Robin Cockett, Richard Garner
Restriction categories were introduced to provide an axiomatic setting for the study of partially defined mappings; they are categories equipped with an operation called restrictio…
A skew-duoidal Eckmann-Hilton argument and quantum categories
Stephen Lack, Ross Street
A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory wh…
Morita contexts as lax functors
Stephen Lack
Monads are well known to be equivalent to lax functors out of the terminal category. Morita contexts are here shown to be lax functors out of the chaotic category with two objects.…
Multitensor lifting and strictly unital higher category theory
Michael Batanin, Denis-Charles Cisinski, Mark Weber
In this article we extend the theory of lax monoidal structures, also known as multitensors, and the monads on categories of enriched graphs that they give rise to. Our first princ…