Theorems · Theorem · category theory

CategoryTheory.StructuredArrow.projectSubobject.congr_simp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {S : D} {T : CategoryTheory.Functor C D} [inst_2 : CategoryTheory.Limits.HasFiniteLimits C]
  [inst_3 : CategoryTheory.Limits.PreservesFiniteLimits T] {A : CategoryTheory.StructuredArrow S T}
  (a a_1 : CategoryTheory.Subobject A),
  a = a_1 → CategoryTheory.StructuredArrow.projectSubobject a = CategoryTheory.StructuredArrow.projectSubobject a_1

Defined in

Mathlib.CategoryTheory.Subobject.Comma

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasFiniteLimitsCategoryTheory.Limits.PreservesFiniteLimits