Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Arrow.forget

{T : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} T] →
    (P Q W : CategoryTheory.MorphismProperty T) →
      [inst_1 : Q.IsMultiplicative] →
        [inst_2 : W.IsMultiplicative] → CategoryTheory.Functor (P.Arrow Q W) (CategoryTheory.Arrow T)

The forgetful functor from the full subcategory of Arrow T defined by P to Arrow T.

Defined in: Mathlib.CategoryTheory.MorphismProperty.Comma
Cited by: 4 results in Mathlib
Foundations: Depth 18 from the axioms · uses propext, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MorphismProperty.IsMultiplicative CategoryTheory.MorphismProperty.IsMultiplicative

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

Cites8

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
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Functor.idstatement and proof · cited by 3,333
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.Arrowstatement · cited by 713
CategoryTheory.MorphismProperty.IsMultiplicativestatement and proof · cited by 332
CategoryTheory.MorphismProperty.Comma.forgetproof · cited by 28
CategoryTheory.MorphismProperty.Arrowstatement · cited by 17

Cited by7

Results whose statement or proof uses this declaration.

TopPair.proj₂proof · cited by 15
TopPair.proj₁proof · cited by 4
CategoryTheory.MorphismProperty.Arrow.Hom.mkstatement and proof · cited by 1
TopPair.HomologyPretheory.Hom.w_app_assocstatement · cited by 0
CategoryTheory.MorphismProperty.Arrow.forget_comp_leftFunc_mapstatement · cited by 0
CategoryTheory.MorphismProperty.Arrow.forget_comp_rightFunc_mapstatement · cited by 0
CategoryTheory.MorphismProperty.Arrow.Hom.mk_homstatement and proof · cited by 0