Homotopy theory of small diagrams over large categories

DOI10.1515/FORUM.2009.009zbMath1162.55014arXivmath/0607117MaRDI QIDQ3617647

William G. Dwyer, Boris Chorny

Publication date: 30 March 2009

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607117

zbMATH Keywords

simplicial setmodel categoryfunctor categoryhomotopy localizationPostnikov towersmall functorgeneralized small object argument

Mathematics Subject Classification ID

Abstract and axiomatic homotopy theory in algebraic topology (55U35) Equivariant homotopy theory in algebraic topology (55P91)

Related Items

On combinatorial model categories ⋮ On homotopy varieties ⋮ Calculus of functors and model categories ⋮ Limits of small functors ⋮ Class-locally presentable and class-accessible categories ⋮ Duality and small functors ⋮ Brown representability for space-valued functors ⋮ Models for the Maclaurin tower of a simplicial functor via a derived Yoneda embedding ⋮ Homotopy theory of relative simplicial presheaves ⋮ A generalization of Quillen's small object argument ⋮ A tower connecting gauge groups to string topology ⋮ The effective model structure and -groupoid objects ⋮ Cross effects and calculus in an unbased setting

Cites Work

• Limits of small functors
• Classifying pro-fibrations and shape fibrations
• Cartesian closed exact completions
• Constructions of factorization systems in categories
• Localization with respect to a class of maps. I: Equivariant localization of diagrams of spaces
• A generalization of Quillen's small object argument
• Calculus of functors and model categories
• Homotopy Theories for Diagrams of Spaces