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Theorems · Theorem · category theory

CategoryTheory.Limits.isIso_of_isTerminal

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (hX : CategoryTheory.Limits.IsTerminal X)
  (hY : CategoryTheory.Limits.IsTerminal Y) (f : X ⟶ Y), CategoryTheory.IsIso f

Any morphism between terminal objects is an isomorphism.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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Around this declaration

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isFlasque_skyscraperSheaf_of_epi_from · cited by 1isFlasque_skyscraperSheaf…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.Limits.IsTerminal.from · cited by 160IsTerminal.fromCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalCategoryTheory.Limits.IsTerminal.hom_ext · cited by 29IsTerminal.hom_extCategoryTheory.Limits.IsTerminal.comp_from · cited by 13IsTerminal.comp_fromCategoryTheory.Limits.IsTerminal.from_self · cited by 9IsTerminal.from_selfLimits.isIso_of_isTerminalCITED BYCITES

Cites10

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Cited by1

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