Model Categories

Hovey, M. (1999). Model Categories. Mathematical Surveys and Monographs.

Type

Book

Intellectual base

Review or monograph

Year

1999

DOI

10.1090/surv/063

ISBN

9780821843611

Link

https://doi.org/10.1090/surv/063

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Homotopy Category
  • characterized by a functor \(\gamma:\mathcal M\to\operatorname{Ho}(\mathcal M)\) that sends every \(w\in W\) to an isomorphism and is universal among functors doing so. Morphisms may be computed by replacing the source cofibrantly and the target fibrantly, then taking the appropriate homotopy classes.
• Quillen Adjunction
  • Equivalently, the right adjoint \(U\) preserves fibrations and trivial fibrations.

    This sourceSection 1.3 is the authoritative source for left/right Quillen functors, equivalent adjoint conditions, derived functors, composition, and Quillen equivalence.

Verification

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Registry ID ref:7560df1211d9 · see in the full table