Theorems · Theorem · category theory
CategoryTheory.CommSq.horiz_inv
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W X Y Z : C} {g : W ⟶ Y} {h : X ⟶ Z} {f : W ≅ X}
{i : Y ≅ Z}, CategoryTheory.CommSq f.hom g h i.hom → CategoryTheory.CommSq f.inv h g i.inv- Defined in
- Mathlib.CategoryTheory.CommSq
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Iso.invstatement · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.CommSqstatement and proof · cited by 158
- CategoryTheory.CommSq.vert_invproof · cited by 11
- CategoryTheory.CommSq.flipproof · cited by 11
Cited by10
Results whose statement or proof uses this declaration.
- groupCohomology.eq_d₀₁_comp_invproof · cited by 4
- groupCohomology.eq_d₁₂_comp_invproof · cited by 3
- groupHomology.eq_d₁₀_comp_invproof · cited by 3
- groupHomology.eq_d₂₁_comp_invproof · cited by 3
- groupCohomology.isoCocycles₂_inv_comp_iCocyclesproof · cited by 2
- groupHomology.isoCycles₂_inv_comp_iCyclesproof · cited by 2
- groupHomology.isoCycles₁_inv_comp_iCyclesproof · cited by 2
- groupCohomology.eq_d₂₃_comp_invproof · cited by 2
- groupCohomology.isoCocycles₁_inv_comp_iCocyclesproof · cited by 2
- groupHomology.eq_d₃₂_comp_invproof · cited by 2