Double loop spaces, braided monoidal categories and algebraic 3-type of space
نویسنده
چکیده
We show that the nerve of a braided monoidal category carries a natural action of a simplicial E2-operad and is thus up to group completion a double loop space. Shifting up dimension twice associates to each braided monoidal category a 1-reduced lax 3-category whose nerve realizes an explicit double delooping whenever all cells are invertible. We deduce that lax 3-groupoids are algebraic models for homotopy 3-types.
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