Search results for "Quillen adjunction"

showing 2 items of 2 documents

Homotopy limits for 2-categories

2008

AbstractWe study homotopy limits for 2-categories using the theory of Quillen model categories. In order to do so, we establish the existence of projective and injective model structures on diagram 2-categories. Using these results, we describe the homotopical behaviour not only of conical limits but also of weighted limits. Finally, pseudo-limits are related to homotopy limits.

Discrete mathematicsPure mathematicsHomotopy lifting propertyHomotopy categoryGeneral MathematicsHomotopyHomotopiaQuillen adjunctionWhitehead theoremCofibrationMathematics::Algebraic Topologyn-connectedCategories (Matemàtica)Mathematics::K-Theory and HomologyHomotopy hypothesisMathematics::Category Theory512 - Àlgebra2-categories homotopy limits coherence conditionsMathematics
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Weighted limits in simplicial homotopy theory

2010

Abstract By combining ideas of homotopical algebra and of enriched category theory, we explain how two classical formulas for homotopy colimits, one arising from the work of Quillen and one arising from the work of Bousfield and Kan, are instances of general formulas for the derived functor of the weighted colimit functor.

Pure mathematicsAlgebra and Number TheoryFunctorBrown's representability theoremHomotopy categoryModel categoryHomotopical algebraHomotopiaQuillen adjunctionCone (category theory)Mathematics::Algebraic TopologyAlgebraCategories (Matemàtica)Homotopy limits simplicial model categories weighted limitsMathematics::K-Theory and HomologyMathematics::Category TheorySimplicial set512 - ÀlgebraMathematics
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