David Roberts
bigroupoid

An internal bigroupoid (in Top, for argument’s sake, but any finitely complete category will do, or at least one with some pullbacks, like Diff) consists of the following data:

  • A space B 0,

  • An internal groupoid B̲ 1=(B 2B 1) equipped with a functor

    (S,T):B̲ 1B 0×B 0,(S,T):\underline{B}_1 \to B_0\times B_0,
  • A (horizontal) composition functor

    B̲ 1× S,B 0,TB̲ 1B̲ 1\underline{B}_1 \times_{S,B_0,T} \underline{B}_1 \to \underline{B}_1

    over B 0×B 0

  • A unit functor

    B 0B̲ 1B_0 \to \underline{B}_1

    over B 0×B 0

  • A (horizontal) inverse functor

    B̲ 1B̲ 1\underline{B}_1 \to \underline{B}_1

    covering the swap map from B 0×B 0 to itself.

Together with natural transformations… (see for the time being Definition 5.21 in my thesis - I need to grok how to do diagrams here)

Revised on October 24, 2012 14:46:09 by David Roberts (121.216.167.70)