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 $\underline{B}_1 = (B_2 \rightrightarrows B_1)$ equipped with a functor$(S,T):\underline{B}_1 \to B_0\times B_0,$
- A (horizontal) composition functor$\underline{B}_1 \times_{S,B_0,T} \underline{B}_1 \to \underline{B}_1$
over $B_0\times B_0$

- A unit functor$B_0 \to \underline{B}_1$
over $B_0\times B_0$

- A (horizontal) inverse functor$\underline{B}_1 \to \underline{B}_1$
covering the swap map from $B_0 \times B_0$ 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)