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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.

CategoryTheory.CommSq.horiz_inv · cited by 10CommSq.horiz_invgroupHomology.π_comp_H1Iso_inv · cited by 2groupHomology.π_comp_H1Is…groupHomology.π_comp_H2Iso_inv · cited by 2groupHomology.π_comp_H2Is…groupHomology.cyclesIso₀_inv_comp_cyclesMap · cited by 2groupHomology.cyclesIso₀_…groupHomology.coinvariantsMk_comp_H0Iso_inv · cited by 2groupHomology.coinvariant…groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv · cited by 2groupHomology.coinvariant…CategoryTheory.BraidedCategory.braiding_inv_naturality_left · cited by 1BraidedCategory.braiding_…CategoryTheory.BraidedCategory.braiding_inv_naturality_right · cited by 1BraidedCategory.braiding_…CategoryTheory.BraidedCategory.braiding_inv_naturality · cited by 1BraidedCategory.braiding_…groupCohomology.δ₀_apply · cited by 0groupCohomology.δ₀_applygroupCohomology.δ₁_apply · cited by 0groupCohomology.δ₁_applyCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.CommSq · cited by 158CategoryTheory.CommSqCategoryTheory.CommSq.w · cited by 122CommSq.wCategoryTheory.Iso.comp_inv_eq · cited by 41Iso.comp_inv_eqCategoryTheory.Iso.eq_inv_comp · cited by 34Iso.eq_inv_compCommSq.vert_invCITED BYCITES

Cites11

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Cited by11

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