Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Comma.opFunctor

{A : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} A] →
    {B : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
        {T : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} T] →
            (L : CategoryTheory.Functor A T) →
              (R : CategoryTheory.Functor B T) →
                CategoryTheory.Functor (CategoryTheory.Comma L R) (CategoryTheory.Comma R.op L.op)ᵒᵖ

The canonical functor from Comma L R to (Comma R.op L.op)ᵒᵖ.

Defined in
Mathlib.CategoryTheory.Comma.Basic
Cited by
11 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.Comma.opEquiv · cited by 7Comma.opEquivCategoryTheory.Comma.opFunctorCompFst · cited by 3Comma.opFunctorCompFstCategoryTheory.Comma.opFunctorCompSnd · cited by 3Comma.opFunctorCompSndCategoryTheory.Comma.final_fst_of_isConnected_structuredArrow · cited by 0Comma.final_fst_of_isConn…CategoryTheory.Comma.final_snd_of_isFiltered_structuredArrow · cited by 0Comma.final_snd_of_isFilt…CategoryTheory.Comma.opEquiv_counitIso · cited by 0Comma.opEquiv_counitIsoCategoryTheory.Comma.opEquiv_functor · cited by 0Comma.opEquiv_functorCategoryTheory.Comma.opEquiv_unitIso · cited by 0Comma.opEquiv_unitIsoCategoryTheory.Comma.opFunctorCompFst_hom_app · cited by 0Comma.opFunctorCompFst_ho…CategoryTheory.Comma.opFunctorCompFst_inv_app · cited by 0Comma.opFunctorCompFst_in…CategoryTheory.Comma.opFunctorCompSnd_hom_app · cited by 0Comma.opFunctorCompSnd_ho…CategoryTheory.Comma.opFunctorCompSnd_inv_app · cited by 0Comma.opFunctorCompSnd_in…CategoryTheory.Comma.opFunctor_map · cited by 0Comma.opFunctor_mapCategoryTheory.Comma.opFunctor_obj · cited by 0Comma.opFunctor_objCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.Functor.op · cited by 997Functor.opCategoryTheory.Comma.left · cited by 886Comma.leftCategoryTheory.Comma.right · cited by 727Comma.rightCategoryTheory.Comma · cited by 566CategoryTheory.CommaCategoryTheory.CommaMorphism.left · cited by 526CommaMorphism.leftCategoryTheory.Comma.hom · cited by 490Comma.homCategoryTheory.CommaMorphism.right · cited by 391CommaMorphism.rightComma.opFunctorCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by14

Results whose statement or proof uses this declaration.