Theorems · Theorem · category theory

CategoryTheory.IsAddMonHom.addMonoidHom_apply

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {M N : C} [inst_2 : CategoryTheory.AddMonObj M] [inst_3 : CategoryTheory.AddMonObj N] (f : M ⟶ N)
  [inst_4 : CategoryTheory.IsAddMonHom f] (X : C) (x : X ⟶ M),
  (CategoryTheory.IsAddMonHom.addMonoidHom f X) x = CategoryTheory.CategoryStruct.comp x f

Defined in: Mathlib.CategoryTheory.Monoidal.Cartesian.Mon
Cited by: 3 results in Mathlib
Foundations: Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory CategoryTheory.AddMonObj CategoryTheory.AddMonObj CategoryTheory.IsAddMonHom

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Cites10

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
CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
AddMonoidHomstatement · cited by 3,230
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
CategoryTheory.AddMonObjstatement and proof · cited by 158
CategoryTheory.IsAddMonHomstatement and proof · cited by 49
CategoryTheory.Hom.addMonoidstatement · cited by 44
CategoryTheory.IsAddMonHom.addMonoidHomstatement and proof · cited by 8

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.IsAddMonHom.addMonoidHom_compproof · cited by 0
CategoryTheory.IsAddMonHom.addMonoidHom_idproof · cited by 0
CategoryTheory.IsAddMonHom.normal_iff_normal_addMonoidHomproof · cited by 0