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Theorems · Definition · category theory

HomotopicalAlgebra.weakEquivalences

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [HomotopicalAlgebra.CategoryWithWeakEquivalences C] → CategoryTheory.MorphismProperty C

The class of weak equivalences in a category with weak equivalences.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations
Cited by
44 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.CategoryWithWeakEquivalences
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HomotopicalAlgebra.trivialCofibrations · cited by 31HomotopicalAlgebra.trivia…HomotopicalAlgebra.trivialFibrations · cited by 30HomotopicalAlgebra.trivia…HomotopicalAlgebra.weakEquivalence_iff · cited by 11HomotopicalAlgebra.weakEq…HomotopicalAlgebra.leftHomotopyClassToHom · cited by 6HomotopicalAlgebra.leftHo…HomotopicalAlgebra.rightHomotopyClassToHom · cited by 4HomotopicalAlgebra.rightH…HomotopicalAlgebra.mem_weakEquivalences · cited by 2HomotopicalAlgebra.mem_we…HomotopicalAlgebra.weakEquivalence_of_postcomp · cited by 2HomotopicalAlgebra.weakEq…HomotopicalAlgebra.weakEquivalence_of_precomp · cited by 2HomotopicalAlgebra.weakEq…HomotopicalAlgebra.weakEquivalence_postcomp_iff · cited by 2HomotopicalAlgebra.weakEq…HomotopicalAlgebra.weakEquivalence_precomp_iff · cited by 2HomotopicalAlgebra.weakEq…HomotopicalAlgebra.bijective_leftHomotopyClassToHom · cited by 2HomotopicalAlgebra.biject…HomotopicalAlgebra.bijective_rightHomotopyClassToHom · cited by 2HomotopicalAlgebra.biject…HomotopicalAlgebra.weakEquivalence_of_postcomp_of_fac · cited by 1HomotopicalAlgebra.weakEq…HomotopicalAlgebra.weakEquivalence_of_precomp_of_fac · cited by 1HomotopicalAlgebra.weakEq…HomotopicalAlgebra.weakEquivalences_op_iff · cited by 1HomotopicalAlgebra.weakEq…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…HomotopicalAlgebra.CategoryWithWeakEquivalences · cited by 77HomotopicalAlgebra.Catego…HomotopicalAlgebra.CategoryWithWeakEquivalences.weakEquivalences · cited by 0CategoryWithWeakEquivalen…HomotopicalAlgebra.weakEquiva…CITED BYCITES

Cites4

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Cited by75

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