Statements (42)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:describedBy |
Homotopical Algebra (Lecture Notes in Mathematics, Vol. 43)
|
| gptkbp:enables |
homotopy limits and colimits
definition of derived functors |
| gptkbp:example |
category of topological spaces
category of spectra category of chain complexes category of differential graded algebras category of simplicial sets |
| gptkbp:field |
gptkb:topology
homotopy theory |
| gptkbp:generalizes |
chain complexes with quasi-isomorphisms
topological spaces with weak homotopy equivalences |
| gptkbp:hasAxiom |
2-out-of-3 property for weak equivalences
closure under retracts factorization axioms lifting properties |
| gptkbp:hasMorphism |
gptkb:Quillen_adjunction
gptkb:Quillen_equivalence |
| https://www.w3.org/2000/01/rdf-schema#label |
Quillen model categories
|
| gptkbp:influenced |
gptkb:model_category_theory
gptkb:∞-categories derived algebraic geometry homotopical algebra |
| gptkbp:introduced |
gptkb:Daniel_Quillen
|
| gptkbp:introducedIn |
1967
|
| gptkbp:purpose |
abstract homotopy theory
|
| gptkbp:referencedIn |
Hovey, M. (1999). Model Categories.
Quillen, D. G. (1967). Homotopical Algebra. Lecture Notes in Mathematics, Vol. 43. Goerss, P. G., & Jardine, J. F. (1999). Simplicial Homotopy Theory. |
| gptkbp:relatedTo |
simplicial sets
model structure |
| gptkbp:structure |
fibrations
cofibrations weak equivalences |
| gptkbp:usedIn |
gptkb:algebraic_geometry
homological algebra higher category theory stable homotopy theory |
| gptkbp:bfsParent |
gptkb:homotopical_algebraic_geometry
gptkb:Homotopical_Algebra_(Grothendieck,_1963) |
| gptkbp:bfsLayer |
8
|