Theorems · Theorem · category theory
CategoryTheory.Limits.IsTerminal.hasTerminal
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} (h : CategoryTheory.Limits.IsTerminal X),
CategoryTheory.Limits.HasTerminal C- Cited by
- 6 results in Mathlib
- Foundations
- Depth 26 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.
Cites16
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.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorproof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Discreteproof · cited by 2,447
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Limits.Cone.ptproof · cited by 1,298
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Discrete.asproof · cited by 269
- CategoryTheory.Limits.IsTerminalstatement and proof · cited by 153
- CategoryTheory.Limits.HasTerminalstatement · cited by 142
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.HasRightKanExtension.mkproof · cited by 2
- CategoryTheory.CardinalDirectedPoset.propSet_singletonproof · cited by 1
- CategoryTheory.Limits.hasLimit_iff_hasTerminal_coneproof · cited by 1
- CategoryTheory.SubobjectRepresentableBy.hasTerminalproof · cited by 1
- CategoryTheory.Limits.hasTerminal_of_hasInitial_opproof · cited by 1
- CategoryTheory.isLeftAdjoint_iff_hasTerminal_costructuredArrowproof · cited by 1