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  • G. M. Kelly
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    Elements 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,
Two-dimensional monad theory
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
Some remarks on Maltsev and Goursat categories
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:
Coherence for compact closed categories
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
Galois theory and a general notion of central extension
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
Elementary observations on 2-categorical limits
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
Reflective subcategories, localizations and factorizationa systems
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
© 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
Notes on enriched categories with colimits of some class (completed version)
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