Theorems · Theorem · category theory
CategoryTheory.CommSq.vert_inv
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W X Y Z : C} {f : W ⟶ X} {i : Y ⟶ Z} {g : W ≅ Y}
{h : X ≅ Z}, CategoryTheory.CommSq f g.hom h.hom i → CategoryTheory.CommSq i g.inv h.inv f- Defined in
- Mathlib.CategoryTheory.CommSq
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 17 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.
Cites11
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.compproof · cited by 17,999
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.CommSqstatement and proof · cited by 158
- CategoryTheory.CommSq.wproof · cited by 122
- CategoryTheory.Iso.comp_inv_eqproof · cited by 41
- CategoryTheory.Iso.eq_inv_compproof · cited by 34
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.CommSq.horiz_invproof · cited by 10
- groupHomology.π_comp_H1Iso_invproof · cited by 2
- groupHomology.π_comp_H2Iso_invproof · cited by 2
- groupHomology.cyclesIso₀_inv_comp_cyclesMapproof · cited by 2
- groupHomology.coinvariantsMk_comp_H0Iso_invproof · cited by 2
- groupHomology.coinvariantsMk_comp_opcyclesIso₀_invproof · cited by 2
- CategoryTheory.BraidedCategory.braiding_inv_naturality_leftproof · cited by 1
- CategoryTheory.BraidedCategory.braiding_inv_naturality_rightproof · cited by 1
- CategoryTheory.BraidedCategory.braiding_inv_naturalityproof · cited by 1
- groupCohomology.δ₀_applyproof · cited by 0
- groupCohomology.δ₁_applyproof · cited by 0