Theorems · Definition · category theory

CategoryTheory.Limits.IsInitial.ofStrict

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.Limits.HasStrictInitialObjects C] →
      {X Y : C} → (X ⟶ Y) → CategoryTheory.Limits.IsInitial Y → CategoryTheory.Limits.IsInitial X

If X ⟶ Y with Y being a strict initial object, then X is also an initial object.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.StrictInitial
Cited by: 0 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasStrictInitialObjects

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Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Iso.symmproof · cited by 993
CategoryTheory.asIsoproof · cited by 177
CategoryTheory.Limits.IsInitialstatement and proof · cited by 158
CategoryTheory.Limits.HasStrictInitialObjectsstatement and proof · cited by 28
CategoryTheory.Limits.IsInitial.ofIsoproof · cited by 15

Cited by1

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CategoryTheory.Limits.IsInitial.ofCoproductDisjointOfCommSqproof · cited by 0