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The formal theory of monads II
Abstract We give an explicit description of the free completion EM ( K ) of a 2-category K under the Eilenberg–Moore construction, and show that this has the same underlying category as theExpand
Adhesive and quasiadhesive categories
We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention toExpand
Adhesive Categories
Adhesive categories are introduced, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved and double-pushout graph rewriting generalises well to rewriting on arbitrary adhesive categories. Expand
Introduction to extensive and distributive categories
Abstract In recent years, there has been considerable discussion as to the appropriate definition of distributive categories. Three definitions which have had some support are: (1) A category withExpand
Restriction categories I: categories of partial maps
It is shown that Par can be made into an equivalence of 2-categories between MCat and a 2-category of restriction categories, and deduce the completeness and cocompleteness of the 2-Categories of M-c categories and of restriction category. Expand
Codescent objects and coherence
Abstract We describe 2-categorical colimit notions called codescent objects of coherence data, and lax codescent objects of lax coherence data, and use them to study the inclusion, T -Alg s →Ps- T -Expand
Hopf monads on monoidal categories
We define Hopf monads on an arbitrary monoidal category, extending the definition given in Bruguieres and Virelizier (2007) [5] for monoidal categories with duals. A Hopf monad is a bimonad (orExpand
A Coherent Approach to Pseudomonads
Abstract The formal theory of monads can be developed in any 2-category, but when it comes to pseudomonads, one is forced to move from 2-categories to Gray-categories (semistrict 3-categories). TheExpand
A 2-Categories Companion
This paper is a rather informal guide to some of the basic theory of 2-categories and bicategories, including notions of limit and colimit, 2-dimensional universal algebra, formal category theory,Expand
2-nerves for bicategories
We describe a Cat-valued nerve of bicategories, which associates to every bicategory a simplicial object in Cat, called the 2-nerve. We define a 2-category NHom whose objects are bicategories andExpand