Theorems · Theorem · category theory

CategoryTheory.Limits.IsInitial.isInitialOfObj.congr_simp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (G : CategoryTheory.Functor C D) (X : C)
  [inst_2 : CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Functor.empty C) G]
  (l l_1 : CategoryTheory.Limits.IsInitial (G.obj X)),
  l = l_1 →
    CategoryTheory.Limits.IsInitial.isInitialOfObj G X l = CategoryTheory.Limits.IsInitial.isInitialOfObj G X l_1

Defined in: Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal
Cited by: 0 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.ReflectsColimit

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Discretestatement · cited by 2,447
CategoryTheory.Limits.IsInitialstatement and proof · cited by 158
CategoryTheory.Functor.emptystatement and proof · cited by 103
CategoryTheory.Limits.ReflectsColimitstatement and proof · cited by 33
CategoryTheory.Limits.IsInitial.isInitialOfObjstatement and proof · cited by 2

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