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Theorems · Definition · category theory

CategoryTheory.Arrow.leftFunc

{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Functor (CategoryTheory.Arrow C) C

The functor sending an arrow to its source.

Defined in
Mathlib.CategoryTheory.Comma.Arrow
Cited by
37 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

TopPair.proj₂ · cited by 15TopPair.proj₂CategoryTheory.Arrow.leftToRight · cited by 10Arrow.leftToRightHomotopicalAlgebra.AttachCells.ofArrowIso · cited by 9AttachCells.ofArrowIsoCategoryTheory.MorphismProperty.FunctorialFactorizationData.i · cited by 7FunctorialFactorizationDa…CategoryTheory.Arrow.leftFunc_map · cited by 5Arrow.leftFunc_mapCategoryTheory.TransfiniteCompositionOfShape.ofArrowIso · cited by 4TransfiniteCompositionOfS…CategoryTheory.SmallObject.relativeCellComplexιObj · cited by 4SmallObject.relativeCellC…CategoryTheory.Limits.ker.ι · cited by 3ker.ιCategoryTheory.SmallObject.relativeCellComplexιObjFObjSuccIso · cited by 3SmallObject.relativeCellC…CategoryTheory.RetractArrow.left · cited by 3RetractArrow.leftCategoryTheory.MorphismProperty.FunctorialFactorizationData.fac · cited by 2FunctorialFactorizationDa…CategoryTheory.ObjectProperty.SerreClassLocalization.hasCokernels · cited by 1SerreClassLocalization.ha…CategoryTheory.ObjectProperty.SerreClassLocalization.hasKernels · cited by 1SerreClassLocalization.ha…CategoryTheory.ComposableArrows.ext₂_of_arrow · cited by 1ComposableArrows.ext₂_of_…CategoryTheory.Functor.mem_mapTriangle_essImage_of_distinguished · cited by 1Functor.mem_mapTriangle_e…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.Arrow · cited by 713CategoryTheory.ArrowCategoryTheory.Comma.fst · cited by 76Comma.fstArrow.leftFuncCITED BYCITES

Cites5

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

Cited by61

Results whose statement or proof uses this declaration.