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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
Defined in
Mathlib.CategoryTheory.GuitartExact.Opposite
Cited by
6 results in Mathlib
Foundations
Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff · cited by 3LocalizerMorphism.isLeftD…CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff_op · cited by 2LocalizerMorphism.isLeftD…CategoryTheory.TwoSquare.GuitartExact.whiskerHorizontal_iff · cited by 1GuitartExact.whiskerHoriz…CategoryTheory.LocalizerMorphism.isRightDerivabilityStructure_iff_op · cited by 1LocalizerMorphism.isRight…CategoryTheory.TwoSquare.GuitartExact.hComp_iff_of_equivalences · cited by 1GuitartExact.hComp_iff_of…CategoryTheory.TwoSquare.GuitartExact.quotient_of_nonempty_rightHomotopy · cited by 0GuitartExact.quotient_of_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.Category.id_comp · cited by 1998Category.id_compQuiver.Hom.op · cited by 1948Hom.opCategoryTheory.Functor.op · cited by 997Functor.opCategoryTheory.Functor.map_id · cited by 616Functor.map_idCategoryTheory.TwoSquare · cited by 100CategoryTheory.TwoSquareTwoSquare.guitartExact_op_iffCITED BYCITES

Cites24

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Cited by6

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