Theorems · Definition · category theory

CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Regular C] →
      {A B : C} →
        (f : A ⟶ B) →
          (A' : CategoryTheory.Subobject A) →
            (B' : CategoryTheory.Subobject B) →
              CategoryTheory.Limits.StrongEpiMonoFactorisation
                (CategoryTheory.CategoryStruct.comp (A' ⊓ (CategoryTheory.Subobject.pullback f).obj B').arrow f)

Given a morphism f : A ⟶ B and subobjects A' ⟶ A and B' ⟶ B, the frobeniusMorphism gives a StrongEpiMonoFactorisation of (A' ⊓ (Subobject.pullback f).obj B').arrow ≫ f through ((«exists» f).obj A' ⊓ B').arrow. This is an auxiliary definition to show frobenius_reciprocity.

Defined in

Mathlib.CategoryTheory.RegularCategory.Basic

Cited by

4 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Regular