Theorems · Inductive type · category theory
HomotopicalAlgebra.ModelCategory
(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type (max u v)A model category is a category equipped with classes of morphisms named cofibrations, fibrations and weak equivalences which satisfy the axioms CM1/CM2/CM3/CM4/CM5 of (closed) model categories.
- Cited by
- 141 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by233
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.BifibrantObject.homRelstatement and proof · cited by 22
- HomotopicalAlgebra.BifibrantObject.HoCatstatement and proof · cited by 20
- HomotopicalAlgebra.BifibrantObject.toHoCatstatement and proof · cited by 20
- HomotopicalAlgebra.CofibrantObject.homRelstatement and proof · cited by 20
- HomotopicalAlgebra.CofibrantObject.HoCatstatement and proof · cited by 17
- HomotopicalAlgebra.CofibrantObject.toHoCatstatement and proof · cited by 14
- HomotopicalAlgebra.CofibrantObject.bifibrantResolutionObjstatement and proof · cited by 13
- HomotopicalAlgebra.FibrantObject.homRelstatement and proof · cited by 12
- HomotopicalAlgebra.CofibrantObject.iBifibrantResolutionObjstatement and proof · cited by 9
- HomotopicalAlgebra.FibrantObject.HoCatstatement and proof · cited by 9
- HomotopicalAlgebra.FibrantObject.toHoCatstatement and proof · cited by 8
- HomotopicalAlgebra.FibrantObject.HoCat.iResolutionObjstatement and proof · cited by 7
Showing the 200 most cited of 233.