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Theorems · Definition · category theory

CategoryTheory.Limits.IsTerminal.ofStrict

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

If X ⟶ Y with Y being a strict terminal object, then X is also a terminal 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.CategoryCategoryTheory.Limits.HasStrictTerminalObjects
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CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.asIso · cited by 177CategoryTheory.asIsoCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalCategoryTheory.Limits.HasStrictTerminalObjects · cited by 17Limits.HasStrictTerminalO…CategoryTheory.Limits.IsTerminal.ofIso · cited by 5IsTerminal.ofIsoIsTerminal.ofStrictCITED BYCITES

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