Stratified model categories

• Autorzy: Jan Spaliński
• Języki publikacji: EN

Abstrakty

EN

The fourth axiom of a model category states that given a commutative square of maps, say i: A → B, g: B → Y, f: A → X, and p: X → Y such that gi = pf, if i is a cofibration, p a fibration and either i or p is a weak equivalence, then a lifting (i.e. a map h: B → X such that ph = g and hi = f) exists. We show that for many model categories the two conditions that either i or p above is a weak equivalence can be embedded in an infinite number of conditions which imply the existence of a lifting (roughly, the weak equivalence condition can be split between i and p). There is a similar modification of the fifth axiom. We call such model categories "stratified" and show that the simplest model categories have this property. Moreover, under some assumptions a category associated to the category of simplicial sets by a family of adjoint functors has this structure. Postnikov decompositions and n-types exist in any such category.

Kategorie tematyczne

• 55U35: Abstract and axiomatic homotopy theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 178
• Numer: 3
• Strony: 217-236

Daty

wydano

2003

Twórcy

autor

Jan Spaliński

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm178-3-3