Add to ORKGThe main objective of this paper is to show that the homotopy colimit of a diagram of quasi-categories and indexed by a small category is a localization of Lurie's higher Grothendieck construction of the diagram. We thereby generalize Thomason's classical result which states that the homotopy colimit of a diagram of categories has the homotopy type of (the classifying space of) the Grothendieck construction of the diagram of categories.Comment: arXiv admin note: text overlap with arXiv:2004.0965
AbstractIn this note we give a model category theoretic interpretation of the homotopy colimit of th...
its simplicial localization yields a “homotopy theory of homotopy theories. ” In this paper we show ...
Abstract. We show that the homotopy colimit construction for diagrams of categories with an operad a...
International audienceGrothendieck introduced in Pursuing Stacks the notion of test category . These...
The homotopy theory of representations of nets of algebras over a (small) category with values in a ...
We prove a version of Quillen's Theorem A for topological categories, and use it to show that under ...
We make use of a higher version of the Yoneda embedding to construct, from a given quasicategory, a ...
This paper explores the relationship amongst the various simplicial and pseudosim-plicial objects ch...
This paper explores the relationship amongst the various simplicial and pseudosim-plicial objects ch...
We use a classical result of McCord and reduction methods of finite spaces to prove a generalization...
We show that the quasicategory defined as the localization of the category of (simple) graphs at the...
In this note, we construct a closed model structure on the category of complexes of projective syste...
Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral...
If all objects of a simplicial combinatorial model category \cat A are cofibrant, then there exists ...
In a sense, noncommutative localization is at the center of homotopy theory, or even more accurately...
AbstractIn this note we give a model category theoretic interpretation of the homotopy colimit of th...
its simplicial localization yields a “homotopy theory of homotopy theories. ” In this paper we show ...
Abstract. We show that the homotopy colimit construction for diagrams of categories with an operad a...
International audienceGrothendieck introduced in Pursuing Stacks the notion of test category . These...
The homotopy theory of representations of nets of algebras over a (small) category with values in a ...
We prove a version of Quillen's Theorem A for topological categories, and use it to show that under ...
We make use of a higher version of the Yoneda embedding to construct, from a given quasicategory, a ...
This paper explores the relationship amongst the various simplicial and pseudosim-plicial objects ch...
This paper explores the relationship amongst the various simplicial and pseudosim-plicial objects ch...
We use a classical result of McCord and reduction methods of finite spaces to prove a generalization...
We show that the quasicategory defined as the localization of the category of (simple) graphs at the...
In this note, we construct a closed model structure on the category of complexes of projective syste...
Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral...
If all objects of a simplicial combinatorial model category \cat A are cofibrant, then there exists ...
In a sense, noncommutative localization is at the center of homotopy theory, or even more accurately...
AbstractIn this note we give a model category theoretic interpretation of the homotopy colimit of th...
its simplicial localization yields a “homotopy theory of homotopy theories. ” In this paper we show ...
Abstract. We show that the homotopy colimit construction for diagrams of categories with an operad a...