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Theorems · Definition · category theory

CategoryTheory.CostructuredArrow.hom

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {S : CategoryTheory.Functor C D} → {T : D} → (X : CategoryTheory.CostructuredArrow S T) → S.obj X.left ⟶ T

The morphism that is part of a costructured arrow.

Defined in
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
Cited by
179 results in Mathlib
Foundations
Depth 25 from the axioms, rests on 125 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.CostructuredArrow.homMk · cited by 55CostructuredArrow.homMkCategoryTheory.Functor.LeftExtension.coconeAt · cited by 20LeftExtension.coconeAtCategoryTheory.OverPresheafAux.restrictedYonedaObj · cited by 17OverPresheafAux.restricte…CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma · cited by 15CostructuredArrow.grothen…CategoryTheory.CostructuredArrow.isoMk · cited by 14CostructuredArrow.isoMkCategoryTheory.Functor.rightKanExtensionCounit · cited by 11Functor.rightKanExtension…CategoryTheory.CostructuredArrow.w · cited by 10CostructuredArrow.wCategoryTheory.CostructuredArrow.preEquivalence.inverse · cited by 9preEquivalence.inverseCategoryTheory.Functor.RightExtension.coneAt · cited by 9RightExtension.coneAtCategoryTheory.Comma.costructuredArrowSndInclusion · cited by 9Comma.costructuredArrowSn…CategoryTheory.Functor.costructuredArrowMapCocone · cited by 8Functor.costructuredArrow…CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor · cited by 8CostructuredArrow.ofComma…CategoryTheory.CostructuredArrow.post · cited by 8CostructuredArrow.postCategoryTheory.OverPresheafAux.counitForward · cited by 8OverPresheafAux.counitFor…CategoryTheory.Bicategory.RightLift.counit · cited by 8RightLift.counitCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.CostructuredArrow · cited by 536CategoryTheory.Costructur…CategoryTheory.Comma.hom · cited by 490Comma.homCategoryTheory.CostructuredArrow.left · cited by 202CostructuredArrow.leftCostructuredArrow.homCITED BYCITES

Cites7

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Cited by236

Results whose statement or proof uses this declaration.