Theorems · Theorem · category theory
CategoryTheory.op_comp
∀ {C : Type u₁} [inst : CategoryTheory.CategoryStruct.{v₁, u₁} C] {X Y Z : C} {f : X ⟶ Y} {g : Y ⟶ Z},
(CategoryTheory.CategoryStruct.comp f g).op = CategoryTheory.CategoryStruct.comp g.op f.op- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- Oppositestatement · cited by 8,081
- Quiver.Hom.opstatement · cited by 1,948
- CategoryTheory.CategoryStructstatement and proof · cited by 343
Cited by72
Results whose statement or proof uses this declaration.
- CategoryTheory.op_invproof · cited by 7
- CategoryTheory.Pseudofunctor.DescentData'.pullHom_pullHom'proof · cited by 4
- CategoryTheory.Functor.IsDenseSubsite.mapPreimage_map_of_facproof · cited by 4
- CategoryTheory.Presieve.isAmalgamation_sieveExtendproof · cited by 4
- CategoryTheory.ShortComplex.cyclesOpIso_inv_naturalityproof · cited by 3
- SSet.mono_of_nonDegenerateproof · cited by 3
- CategoryTheory.Presieve.isSheafFor_subsieve_auxproof · cited by 3
- CategoryTheory.Presieve.is_compatible_of_exists_amalgamationproof · cited by 2
- CategoryTheory.Subfunctor.family_of_elements_compatibleproof · cited by 2
- CategoryTheory.Precoverage.isSheaf_toGrothendieck_iffproof · cited by 2
- AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_appproof · cited by 2