Theorems · Theorem · category theory
CategoryTheory.TwoSquare.guitartExact_op_iff
∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} {C₄ : Type u₄} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
[inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
[inst_3 : CategoryTheory.Category.{v₄, u₄} C₄] {T : CategoryTheory.Functor C₁ C₂} {L : CategoryTheory.Functor C₁ C₃}
{R : CategoryTheory.Functor C₂ C₄} {B : CategoryTheory.Functor C₃ C₄} (w : CategoryTheory.TwoSquare T L R B),
w.op.GuitartExact ↔ w.GuitartExact- Cited by
- 6 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- Quiver.Hom.opproof · cited by 1,948
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iffproof · cited by 3
- CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff_opproof · cited by 2
- CategoryTheory.TwoSquare.GuitartExact.whiskerHorizontal_iffproof · cited by 1
- CategoryTheory.LocalizerMorphism.isRightDerivabilityStructure_iff_opproof · cited by 1
- CategoryTheory.TwoSquare.GuitartExact.hComp_iff_of_equivalencesproof · cited by 1
- CategoryTheory.TwoSquare.GuitartExact.quotient_of_nonempty_rightHomotopyproof · cited by 0