Theorems · Theorem · category theory
CategoryTheory.CommSq.unop
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W X Y Z : Cᵒᵖ} {f : W ⟶ X} {g : W ⟶ Y} {h : X ⟶ Z}
{i : Y ⟶ Z}, CategoryTheory.CommSq f g h i → CategoryTheory.CommSq i.unop h.unop g.unop f.unopThe commutative square associated to a commutative square in the opposite category.
- Defined in
- Mathlib.CategoryTheory.CommSq
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- 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.CategoryStruct.compproof · cited by 17,999
- Oppositestatement and proof · cited by 8,081
- Opposite.unopstatement · cited by 2,231
- Quiver.Hom.unopstatement and proof · cited by 903
- CategoryTheory.CommSqstatement and proof · cited by 158
- CategoryTheory.CommSq.wproof · cited by 122
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.CommSq.LiftStruct.unopstatement · cited by 3
- CategoryTheory.CommSq.LiftStruct.unopEquivstatement · cited by 3
- CategoryTheory.CommSq.coconeUnopstatement · cited by 1
- CategoryTheory.CommSq.coneUnopstatement · cited by 1
- CategoryTheory.CommSq.LiftStruct.unopEquiv_applystatement · cited by 0
- CategoryTheory.CommSq.LiftStruct.unopEquiv_symm_applystatement and proof · cited by 0
- CategoryTheory.CommSq.LiftStruct.unop_lstatement · cited by 0
- CategoryTheory.CommSq.HasLift.iff_unopstatement and proof · cited by 0
- CategoryTheory.CommSq.LiftStruct.opEquiv_symm_applystatement · cited by 0