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THE SPAN CONSTRUCTION
"... Abstract. We present two generalizations of the Span construction. The first generalization ..."
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Abstract. We present two generalizations of the Span construction. The first generalization
A THOMASON MODEL STRUCTURE ON THE CATEGORY
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"... Abstract. We construct a cofibrantly generated Thomason model structure on the category of small nfold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An nfold functor is a weak equivalence if and only if the diagonal of its n ..."
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Abstract. We construct a cofibrantly generated Thomason model structure on the category of small nfold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An nfold functor is a weak equivalence if and only if the diagonal of its nfold nerve is a weak equivalence of simplicial sets. We introduce an nfold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the nfold nerve. As a consequence, the unit and counit of the adjunction between simplicial sets and nfold categories are natural weak equivalences.
A MODEL STRUCTURE ON INTERNAL CATEGORIES IN SIMPLICIAL SETS
"... Abstract. We put a model structure on the category of categories internal to simplicial sets. The weak equivalences in this model structure are preserved and reflected by the nerve functor to bisimplicial sets with the complete Segal space model structure. This model structure is shown to be a mod ..."
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Abstract. We put a model structure on the category of categories internal to simplicial sets. The weak equivalences in this model structure are preserved and reflected by the nerve functor to bisimplicial sets with the complete Segal space model structure. This model structure is shown to be a model for the homotopy theory of infinity categories. We also study the homotopy theory of internal presheaves over an internal category.