Theorems · Theorem · category theory

CategoryTheory.MonObj.pow_comp

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {M N X : C} [inst_2 : CategoryTheory.MonObj M] [inst_3 : CategoryTheory.MonObj N] (f : X ⟶ M) (n : ℕ) (g : M ⟶ N)
  [CategoryTheory.IsMonHom g], CategoryTheory.CategoryStruct.comp (f ^ n) g = CategoryTheory.CategoryStruct.comp f g ^ n

Defined in: Mathlib.CategoryTheory.Monoidal.Cartesian.Mon
Cited by: 1 results in Mathlib
Foundations: Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory CategoryTheory.MonObj CategoryTheory.MonObj CategoryTheory.IsMonHom

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Cites11

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.CategoryStruct.compstatement and proof · cited by 17,999
pow_zeroproof · cited by 1,094
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
pow_succproof · cited by 374
CategoryTheory.MonObjstatement and proof · cited by 199
CategoryTheory.IsMonHomstatement and proof · cited by 56
CategoryTheory.Hom.monoidstatement · cited by 52
CategoryTheory.MonObj.mul_compproof · cited by 3
CategoryTheory.MonObj.one_compproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MonObj.pow_comp_assocproof · cited by 0