Theorems · Theorem · category theory

AddMonCat.comp_apply

∀ {M N T : AddMonCat} (f : M ⟶ N) (g : N ⟶ T) (x : ↑M),
  (CategoryTheory.ConcreteCategory.hom (CategoryTheory.CategoryStruct.comp f g)) x =
    (CategoryTheory.ConcreteCategory.hom g) ((CategoryTheory.ConcreteCategory.hom f) x)

Defined in: Mathlib.Algebra.Category.MonCat.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 19 from the axioms · uses propext, Quot.sound

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Cites8

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

DFunLike.coestatement and proof · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
AddMonoidHomstatement · cited by 3,230
AddMonCatstatement and proof · cited by 71
AddMonCat.carrierstatement and proof · cited by 60
AddMonCat.Hom.homproof · cited by 21

Cited by1

Results whose statement or proof uses this declaration.

AddMonCat.FilteredColimits.colimitAddAux_eq_of_rel_rightproof · cited by 0