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homotopy 2-category

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higher category theory

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Idea

The homotopy 2-category of an (∞,n)-category 𝒞\mathcal{C} is the 2-category Ho 2(𝒞)Ho_2(\mathcal{C}) with the same objects and 1-morphisms as 𝒞\mathcal{C} and with the 2-morphisms being the equivalence classes of 2-morphisms of 𝒞\mathcal{C}.

In other words, for every pair X,YX,Y of objects in 𝒞\mathcal{C}, the hom-category Ho 2(𝒞)(X,Y)Ho_2(\mathcal{C})(X,Y) is the ordinary homotopy category of the (,n1)(\infty,n-1)-category 𝒞(X,Y)\mathcal{C}(X,Y).

Created on August 23, 2012 16:32:42 by Urs Schreiber (131.174.41.87)