Theorems · Theorem · category theory

CategoryTheory.Limits.pullback_inv_fst_snd_of_right_isIso

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z)
  [inst_1 : CategoryTheory.IsIso g],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.inv (CategoryTheory.Limits.pullback.fst f g))
      (CategoryTheory.Limits.pullback.snd f g) =
    CategoryTheory.CategoryStruct.comp f (CategoryTheory.inv g)

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso
Cited by: 2 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.IsIso

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Cites13

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
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.IsIsostatement and proof · cited by 1,156
CategoryTheory.Limits.pullbackstatement and proof · cited by 864
CategoryTheory.Limits.pullback.fststatement and proof · cited by 639
CategoryTheory.Limits.pullback.sndstatement and proof · cited by 637
CategoryTheory.invstatement and proof · cited by 467
CategoryTheory.IsIso.hom_inv_idproof · cited by 97
CategoryTheory.Limits.pullback.condition_assocproof · cited by 24
CategoryTheory.IsIso.inv_comp_eqproof · cited by 12

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.pullback_lift_diagonal_isPullbackproof · cited by 1
CategoryTheory.Limits.pullback_inv_fst_snd_of_right_isIso_assocproof · cited by 0