nLab Charles Ehresmann

Selected writings

Charles Ehresmann was a pioneer in investigating groupoids and then categories for their applications in geometric problems. It is notable that he was a student of Elie Cartan, famous for his work in Analysis. As a consequence, Ehresmann was fascinated by local-to-global problems, which are among the key problems in mathematics and science. This is one reason for his approach to category theory being different from that in the USA, where category theory was founded.

He had a succession of influential students, and among the concepts which he initiated are: fibre bundles, foliations, germs, gerbes, double categories, sketches, topological groupoids, Lie groupoids, holonomy, structured categories.

The journal he founded and edited, Cahiers de Topologie et Géométrie Différentielle Catégoriques, has been continued by his widow, Andree Ehresmann.

  • English Wikipedia page

  • Wikipédia français

  • MacTutor biography

  • “The mathematical legacy of Charles Ehresmann”, conference “Geometry and Topology of Manifolds” Bedlewo 2005, Editors: Jan Kubarski, Jean Pradines, Tomasz Rybicki and Robert Wolak, Institute of mathematics, Polish academy of sciences, Banach center publications 76 (2007).

Selected writings

Collected works:

Introducing the notion of Ehresmann connections and proving Ehresmann's theorem:

Early proposal to grasp the notion of mathematical structure via category theory, specifically in terms of forgetful functors between the groupoids which they form (cf. stuff, structure, property):

Introduction of the notion of double category:

Introducing the notion of topological groupoids and Lie groupoids:

  • Charles Ehresmann, Catégories topologiques et categories différentiables, Colloque de Géométrie différentielle globale, Bruxelles, C.B.R.M., (1959) pp. 137-150 (pdf, zbMath:0205.28202)

Introducing the notion of internal categories (or at least something in this direction):

Introducing sketches:

  • Charles Ehresmann, Esquisses et types de structures algébriques, Bul. Inst. Polit. Iasi 14 1–2 (1968) 1-14 [pdf]

On internalization of mathematical structures via sketches:

category: people

Last revised on February 1, 2024 at 10:49:34. See the history of this page for a list of all contributions to it.