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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 the… Expand

Adhesive and quasiadhesive categories

- S. Lack, P. Sobocinski
- Mathematics, Computer Science
- RAIRO Theor. Informatics Appl.
- 1 July 2005

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 to… Expand

Adhesive Categories

- S. Lack, P. Sobocinski
- Computer Science
- FoSSaCS
- 2004

TLDR

Introduction to extensive and distributive categories

- A. Carboni, S. Lack, R. Walters
- Mathematics
- 3 February 1993

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 with… Expand

Restriction categories I: categories of partial maps

- J. Cockett, S. Lack
- Computer Science, Mathematics
- Theor. Comput. Sci.
- 6 January 2002

TLDR

Codescent objects and coherence

- S. Lack
- Mathematics
- 8 November 2002

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

- A. Bruguières, S. Lack, A. Virelizier
- Mathematics
- 9 March 2010

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 (or… Expand

A Coherent Approach to Pseudomonads

- S. Lack
- Mathematics
- 25 June 2000

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). The… Expand

A 2-Categories Companion

- S. Lack
- Mathematics
- 19 February 2007

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 and… Expand

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