5,603 research outputs found
Three themes in the work of Charles Ehresmann: Local-to-global; Groupoids; Higher dimensions
This paper illustrates the themes of the title in terms of: van Kampen type
theorems for the fundamental groupoid; holonomy and monodromy groupoids; and
higher homotopy groupoids. Interaction with work of the writer is explored.Comment: 13 pages; Expansion of an invited talk given to the 7th Conference on
the Geometry and Topology of Manifolds: The Mathematical Legacy of Charles
Ehresmann, Bedlewo 8.05.2005-15.05.2005 (Poland) Version 2: corrections of a
date and some grammar, slight referencing changes, and a small comment added
Version4. Theorem 2.2 got corrected and then uncorrected! It is now
corrected. Version5. Reference added. Various minor improvements made in
reaction to comment
Double groupoids, matched pairs and then matched triples
In this note we show that the known relation between double groupoids and
matched pairs of groups may be extended, or seems to extend, to the triple
case. The references give some other occurrences of double groupoids.Comment: 5 page
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