David Roberts bigroupoid

Redirected from "model structure on SSet-categories".

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

  • A space B 0B_0,
  • An internal groupoid B̲ 1=(B 2B 1)\underline{B}_1 = (B_2 \rightrightarrows B_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 0B_0\times B_0

  • A unit functor
    B 0B̲ 1 B_0 \to \underline{B}_1

    over B 0×B 0B_0\times B_0

  • A (horizontal) inverse functor
    B̲ 1B̲ 1 \underline{B}_1 \to \underline{B}_1

    covering the swap map from B 0×B 0B_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)

Last revised on October 24, 2012 at 14:46:09. See the history of this page for a list of all contributions to it.