Short Introduction to Enriched Categories

Francis Borceux (1) , Isar Stubbe (2)

1 UCL - Université Catholique de Louvain = Catholic University of Louvain
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

This text aims to be a short introduction to some of the basic notions in ordinary and enriched category theory. With reasonable detail but always in a compact fashion, we have brought together in the first part of this paper the definitions and basic properties of such notions as limit and colimit constructions in a category, adjoint functors between categories, equivalences and monads. In the second part we pass on to enriched category theory: it is explained how one can "replace" the category of sets and mappings, which plays a crucial role in ordinary category theory, by a more general symmetric monoidal closed category, and how most results of ordinary category theory can be translated to this more general setting. For a lack of space we had to omit detailed proofs, but instead we have included lots of examples which we hope will be helpful. In any case, the interested reader will find his way to the references, given at the end of the paper.

Domaines: Mathématiques [math]; Informatique [cs]; Physique [physics]

Francis Borceux, Isar Stubbe. Short Introduction to Enriched Categories. Bob Coecke; David Moore; Alexander Wilce. Current Research in Operational Quantum Logic. Algebras, Categories, Languages, 111, Springer Netherlands, pp.167-194, 2000, Fundamental Theories of Physics, 978-90-481-5437-1. ⟨10.1007/978-94-017-1201-9_7⟩. ⟨hal-03606892⟩