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, 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.
C. Ehresmann, 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.
“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).
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