Theorems · Theorem · category theory

CategoryTheory.MonoOver.commSqOfHasStrongEpiMonoFactorisation

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {Y : C} [inst_1 : CategoryTheory.Limits.HasCoproducts C]
  [inst_2 : CategoryTheory.Limits.HasStrongEpiMonoFactorisations C] {J : Type u₂}
  [inst_3 : CategoryTheory.Category.{v₂, u₂} J] (F : CategoryTheory.Functor J (CategoryTheory.MonoOver Y))
  (c : CategoryTheory.Limits.Cocone F),
  CategoryTheory.CommSq (CategoryTheory.Limits.Sigma.desc fun i => CategoryTheory.Over.Hom.left (c.ι.app i).hom)
    (CategoryTheory.MonoOver.strongEpiMonoFactorisationSigmaDesc F).e c.pt.arrow
    (CategoryTheory.MonoOver.strongEpiMonoFactorisationSigmaDesc F).m

Defined in

Mathlib.CategoryTheory.Subobject.MonoOver

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.Limits.HasStrongEpiMonoFactorisationsCategoryTheory.Category