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Theorems · Definition · category theory

CategoryTheory.CostructuredArrow.proj

{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.Functor (CategoryTheory.CostructuredArrow S T) C

The obvious projection functor from costructured arrows.

Defined in
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
Cited by
122 results in Mathlib
Foundations
Depth 25 from the axioms, rests on 131 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.Functor.LeftExtension.coconeAt · cited by 20LeftExtension.coconeAtCategoryTheory.Functor.pointwiseLeftKanExtension · cited by 19Functor.pointwiseLeftKanE…CategoryTheory.Functor.pointwiseLeftKanExtensionUnit · cited by 16Functor.pointwiseLeftKanE…CategoryTheory.Functor.HasPointwiseLeftKanExtensionAt · cited by 13Functor.HasPointwiseLeftK…CategoryTheory.Functor.leftKanExtensionObjIsoColimit · cited by 10Functor.leftKanExtensionO…CategoryTheory.Functor.costructuredArrowMapCocone · cited by 8Functor.costructuredArrow…CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.functor · cited by 6ofCostructuredArrowProjEq…CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse · cited by 6ofCostructuredArrowProjEq…CategoryTheory.CostructuredArrow.ofDiagEquivalence.functor · cited by 6ofDiagEquivalence.functorCategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.functorToInterchange · cited by 5PreservesFiniteLimitsOfIs…TopCat.Presheaf.pullbackObjObjOfImageOpen · cited by 5Presheaf.pullbackObjObjOf…CategoryTheory.Functor.pointwiseLeftKanExtensionUnit_app · cited by 5Functor.pointwiseLeftKanE…CategoryTheory.Functor.pointwiseLeftKanExtension_desc_app · cited by 5Functor.pointwiseLeftKanE…CategoryTheory.CostructuredArrow.ιCompGrothendieckProj · cited by 5CostructuredArrow.ιCompGr…Profinite.Extend.cocone · cited by 5Extend.coconeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.fromPUnit · cited by 769Functor.fromPUnitCategoryTheory.CostructuredArrow · cited by 536CategoryTheory.Costructur…CategoryTheory.Comma.fst · cited by 76Comma.fstCostructuredArrow.projCITED BYCITES

Cites5

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

Cited by175

Results whose statement or proof uses this declaration.