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Theorems · Theorem · category theory

CategoryTheory.Limits.IsTerminal.hom_ext

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (t : CategoryTheory.Limits.IsTerminal X)
  (f g : Y ⟶ X), f = g

Any two morphisms to a terminal object are equal.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
Cited by
29 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Limits.IsTerminal.comp_from · cited by 13IsTerminal.comp_fromCategoryTheory.Limits.IsTerminal.from_self · cited by 9IsTerminal.from_selfAlgebraicGeometry.quasiSeparatedSpace_of_quasiSeparated · cited by 3AlgebraicGeometry.quasiSe…isPullbackOfIsTerminalIsProduct · cited by 3isPullbackOfIsTerminalIsP…SSet.Quasicategory.hasLiftingProperty · cited by 2Quasicategory.hasLiftingP…TopCat.Presheaf.isSheaf_of_isTerminal_of_indiscrete · cited by 2Presheaf.isSheaf_of_isTer…CategoryTheory.Limits.IsTerminal.strict_hom_ext · cited by 2IsTerminal.strict_hom_extSSet.quasicategory_of_hasLiftingProperty · cited by 2SSet.quasicategory_of_has…CategoryTheory.Functor.final_const_of_isTerminal · cited by 1Functor.final_const_of_is…CategoryTheory.CostructuredArrow.IsUniversal.hom_desc · cited by 1IsUniversal.hom_descCategoryTheory.Subobject.Classifier.χ_pullback_obj_mk_truth_arrow · cited by 1Classifier.χ_pullback_obj…CategoryTheory.Endofunctor.Coalgebra.Terminal.right_inv' · cited by 1Terminal.right_inv'CategoryTheory.Limits.isIso_of_isTerminal · cited by 1Limits.isIso_of_isTerminalisBinaryProductOfIsTerminalIsPullback · cited by 1isBinaryProductOfIsTermin…CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_fst · cited by 1BinaryFan.isLimit_iff_isI…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalCategoryTheory.Limits.IsLimit.hom_ext · cited by 43IsLimit.hom_extIsTerminal.hom_extCITED BYCITES

Cites4

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Cited by32

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