Theorems · Theorem · category theory

CategoryTheory.IsMonHom.isNormalHom_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {G H : C} [inst_2 : CategoryTheory.GrpObj G] [inst_3 : CategoryTheory.GrpObj H] {φ : H ⟶ G}
  [CategoryTheory.IsMonHom φ] [CategoryTheory.Mono φ],
  CategoryTheory.IsMonHom.Normal φ ↔
    ∃ ψ,
      CategoryTheory.CategoryStruct.comp ψ φ =
        CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft G φ)
          (CategoryTheory.GrpObj.conj G)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Normal

Cited by

1 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.GrpObjCategoryTheory.GrpObjCategoryTheory.IsMonHomCategoryTheory.Mono