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BASIC CONCEPTS OF ENRICHED CATEGORY THEORY

- G. M. Kelly
- PhilosophyElements of ∞-Category Theory
- 31 January 2022

Although numerous contributions from divers authors, over the past fifteen years or so, have brought enriched category theory to a developed state, there is still no connected account of the theory,… Expand

Two-dimensional monad theory

- R. Blackwell, G. M. Kelly, A. Power
- Mathematics
- 25 July 1989

Abstract We consider a 2-monad T with rank on a complete and cocomplete 2-category, and write T-Alg for the 2-category given the T-algebras, the morphisms preserving the structure to within coherent… Expand

Some remarks on Maltsev and Goursat categories

- A. Carboni, G. M. Kelly, M. Pedicchio
- Mathematics, Computer ScienceAppl. Categorical Struct.
- 1 December 1993

Our aim is to analyze and to publicize two interesting properties — well known in universal algebra for varieties — that a regular category, and in particular an exact category, may possess:… Expand

Coherence for compact closed categories

- G. M. Kelly, M. Laplaza
- Mathematics
- 1 December 1980

It gives us great pleasure to honour, on the occasion of his seventieth birthday, our friend and mentor Saunders MacLane; and to acknowledge that our interest in coherence problems stems from his… Expand

Galois theory and a general notion of central extension

- G. Janelidze, G. M. Kelly
- Mathematics
- 25 November 1994

Abstract We propose a theory of central extensions for universal algebras, and more generally for objects in an exact category C , centrality being defined relatively to an “admissible” full… Expand

Elementary observations on 2-categorical limits

- G. M. Kelly
- Mathematics
- 1 April 1989

With a view to further applications, we give a self-contained account of indexed limits for 2-categories, including necessary and sufficient conditions for 2-categorical completeness. Many important… Expand

Reflective subcategories, localizations and factorizationa systems

- C. Cassidy, M. Hébert, G. M. Kelly
- Mathematics
- 1 June 1985

This work is a detailed analysis of the relationship between reflective subcategories of a category and factorization systems supported by the category.

Structures defined by finite limits in the enriched context, I

- G. M. Kelly
- Mathematics
- 1982

© Andrée C. Ehresmann et les auteurs, 1982, tous droits réservés. L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec les… Expand

Notes on enriched categories with colimits of some class (completed version)

- G. M. Kelly, V.Schmitt
- Mathematics
- 22 January 2005

The paper is in essence a survey of categories having $\phi$-weighted colimits for all the weights $\phi$ in some class $\Phi$. We introduce the class $\Phi^+$ of {\em $\Phi$-flat} weights which are… Expand

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