Stratified model categories

Jan Spaliński. "Stratified model categories." Fundamenta Mathematicae 178.3 (2003): 217-236. <http://eudml.org/doc/282636>.

@article{JanSpaliński2003,
abstract = {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.},
author = {Jan Spaliński},
journal = {Fundamenta Mathematicae},
keywords = {stratified model category; weak equivalence; fibration; cofibration; Postnikov decomposition; -type},
language = {eng},
number = {3},
pages = {217-236},
title = {Stratified model categories},
url = {http://eudml.org/doc/282636},
volume = {178},
year = {2003},
}

TY - JOUR
AU - Jan Spaliński
TI - Stratified model categories
JO - Fundamenta Mathematicae
PY - 2003
VL - 178
IS - 3
SP - 217
EP - 236
AB - 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.
LA - eng
KW - stratified model category; weak equivalence; fibration; cofibration; Postnikov decomposition; -type
UR - http://eudml.org/doc/282636
ER -