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Theorems · Definition · category theory

CategoryTheory.CostructuredArrow.left

{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} → CategoryTheory.CostructuredArrow S T → C

The left object of a costructured arrow.

Defined in
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
Cited by
202 results in Mathlib
Foundations
Depth 24 from the axioms, rests on 122 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.hom · cited by 179CostructuredArrow.homCategoryTheory.CostructuredArrow.homMk · cited by 55CostructuredArrow.homMkCategoryTheory.Functor.LeftExtension.coconeAt · cited by 20LeftExtension.coconeAtCategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma · cited by 15CostructuredArrow.grothen…CategoryTheory.CostructuredArrow.isoMk · cited by 14CostructuredArrow.isoMkCategoryTheory.Bicategory.RightLift.lift · cited by 13RightLift.liftCategoryTheory.Functor.rightKanExtension · cited by 11Functor.rightKanExtensionCategoryTheory.CostructuredArrow.eqToHom_left · cited by 10CostructuredArrow.eqToHom…CategoryTheory.CostructuredArrow.preEquivalence.inverse · cited by 9preEquivalence.inverseCategoryTheory.Functor.RightExtension.coneAt · cited by 9RightExtension.coneAtCategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence · cited by 9CategoryOfElements.costru…CategoryTheory.Comma.costructuredArrowSndInclusion · cited by 9Comma.costructuredArrowSn…CategoryTheory.Functor.costructuredArrowMapCocone · cited by 8Functor.costructuredArrow…CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor · cited by 8CostructuredArrow.ofComma…CategoryTheory.OverPresheafAux.counitForward · cited by 8OverPresheafAux.counitFor…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Comma.left · cited by 886Comma.leftCategoryTheory.CostructuredArrow · cited by 536CategoryTheory.Costructur…CostructuredArrow.leftCITED BYCITES

Cites4

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Cited by261

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