Theorems · Theorem · category theory

CategoryTheory.Arrow.leftFunc_map

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  {X Y : CategoryTheory.Comma (CategoryTheory.Functor.id C) (CategoryTheory.Functor.id C)} (f : X ⟶ Y),
  CategoryTheory.Arrow.leftFunc.map f = f.left

Defined in: Mathlib.CategoryTheory.Comma.Arrow
Cited by: 5 results in Mathlib
Foundations: Depth 18 from the axioms · uses propext, Quot.sound
Assumes: CategoryTheory.Category

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Cites9

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.mapstatement and proof · cited by 8,698
CategoryTheory.Functor.idstatement and proof · cited by 3,333
CategoryTheory.Comma.leftstatement · cited by 886
CategoryTheory.Arrowstatement · cited by 713
CategoryTheory.Commastatement and proof · cited by 566
CategoryTheory.CommaMorphism.leftstatement · cited by 526
CategoryTheory.Arrow.leftFuncstatement and proof · cited by 37

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.ObjectProperty.SerreClassLocalization.hasCokernelsproof · cited by 1
CategoryTheory.ObjectProperty.SerreClassLocalization.hasKernelsproof · cited by 1
CategoryTheory.ObjectProperty.SerreClassLocalization.preservesFiniteColimits_comp_iffproof · cited by 1
CategoryTheory.ObjectProperty.SerreClassLocalization.preservesFiniteLimits_comp_iffproof · cited by 1
HomotopicalAlgebra.nonempty_attachCells_iffproof · cited by 0