nLab Charles Ehresmann

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:

• Œuvres complètes et commentées

  I-1,2. Topologie algébrique et géométrie différentielle, With commentary by Willem van Est, Michel Zisman, Georges Reeb, Paulette Libermann, René Thom, Jean Pradines, Robert Hermann, Anders Kock, André Haefliger, Jean Bénabou, René Guitart, and Andrée Charles Ehresmann, Edited by Andrée Charles Ehresmann, Cahiers Topologie Géométrie Différentielle, 24, (1983) suppll. 1.

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

• Charles Ehresmann, Les connexions infinitésimales dans un espace fibré différentiable,

  Colloque de topologie (espaces fibrés), Bruxelles, 1950, Georges Thone, Liège; Masson et Cie., Paris (1951) 29–55

  Séminaire Bourbaki, 1 24 (1952) 153–168 [numdam:SB_1948-1951__1__153_0, pdf]

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):

• Charles Ehresmann, Gattungen in Lokalen Strukturen, Jahresbericht der Deutschen Mathematiker-Vereinigung 60 (1958) 49-77 [dml:146434]

• Charles Ehresmann, Catégories et Structures, Séminaire Ehresmann. Topologie et géométrie différentielle 6 (1964) 1-31 [numdam:SE_1964__6__A8_0, dml:112200]

Introduction of the notion of double category:

• Charles Ehresmann, Catégories double et catégories structurées, C.R. Acad. Paris 256 (1963) 1198-1201 [pdf, gallica]

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):

• Charles Ehresmann, Catégories structurées, Annales scientifiques de l’École Normale Supérieure, Série 3, Tome 80 (1963) no. 4, pp. 349-426 (numdam:ASENS_1963_3_80_4_349_0)

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:

• Andrée Bastiani, Charles Ehresmann, Categories of sketched structures, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 13 (1972) no. 2, pp. 104-214 (numdam:CTGDC_1972__13_2_104_0)

category: people