Theorems · Definition · category theory

HomotopicalAlgebra.BifibrantObject.mk

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : HomotopicalAlgebra.CategoryWithCofibrations C] →
      [inst_2 : CategoryTheory.Limits.HasInitial C] →
        [inst_3 : HomotopicalAlgebra.CategoryWithFibrations C] →
          [inst_4 : CategoryTheory.Limits.HasTerminal C] →
            (X : C) →
              [HomotopicalAlgebra.IsCofibrant X] →
                [HomotopicalAlgebra.IsFibrant X] → HomotopicalAlgebra.BifibrantObject C

Constructor for BifibrantObject C.

Defined in: Mathlib.AlgebraicTopology.ModelCategory.Bifibrant
Cited by: 15 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithCofibrations CategoryTheory.Limits.HasInitial HomotopicalAlgebra.CategoryWithFibrations CategoryTheory.Limits.HasTerminal HomotopicalAlgebra.IsCofibrant HomotopicalAlgebra.IsFibrant

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Limits.HasInitialstatement and proof · cited by 185
CategoryTheory.Limits.HasTerminalstatement and proof · cited by 142
HomotopicalAlgebra.IsCofibrantstatement and proof · cited by 56
HomotopicalAlgebra.IsFibrantstatement and proof · cited by 56
HomotopicalAlgebra.CategoryWithFibrationsstatement and proof · cited by 46
HomotopicalAlgebra.CategoryWithCofibrationsstatement and proof · cited by 46
HomotopicalAlgebra.BifibrantObjectstatement · cited by 38

Cited by18

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.BifibrantObject.homMkstatement · cited by 14
HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRightstatement and proof · cited by 4
HomotopicalAlgebra.bijective_rightHomotopyClassToHomproof · cited by 2
HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeftstatement · cited by 1
HomotopicalAlgebra.BifibrantObject.homMk_homMkstatement · cited by 1
HomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'_appstatement · cited by 0
HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_appstatement · cited by 0
HomotopicalAlgebra.BifibrantObject.inverts_iff_factorsproof · cited by 0
HomotopicalAlgebra.BifibrantObject.mk_surjectivestatement · cited by 0
HomotopicalAlgebra.CofibrantObject.exists_bifibrantproof · cited by 0
HomotopicalAlgebra.BifibrantObject.weakEquivalence_homMk_iffstatement · cited by 0
HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_applystatement · cited by 0