Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
category theory concept |
| gptkbp:enables |
abstract homotopy theory
definition of homotopy category |
| gptkbp:generalizes |
topological spaces with weak homotopy equivalences, Serre fibrations, and cofibrations
model ∞-category |
| gptkbp:hasApplication |
gptkb:algebraic_geometry
homological algebra simplicial sets stable homotopy theory chain complexes derived functors |
| gptkbp:hasAxiom |
three distinguished classes of morphisms
|
| gptkbp:hasClassOfMorphisms |
fibrations
cofibrations weak equivalences |
| gptkbp:hasProperty |
factorization axiom
lifting axiom two-out-of-three property for weak equivalences |
| https://www.w3.org/2000/01/rdf-schema#label |
Quillen model category
|
| gptkbp:introduced |
gptkb:Daniel_Quillen
|
| gptkbp:introducedIn |
1967
|
| gptkbp:referencedIn |
gptkb:Quillen,_D._G.,_Homotopical_Algebra,_Lecture_Notes_in_Mathematics,_Vol._43,_Springer,_1967
|
| gptkbp:usedIn |
gptkb:topology
gptkb:category_theory homotopical algebra |
| gptkbp:bfsParent |
gptkb:Daniel_Quillen
|
| gptkbp:bfsLayer |
7
|