Theorems · Inductive type · category theory
CategoryTheory.Limits.HasStrictTerminalObjects
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropWe say C has strict terminal objects if every terminal object is strict, i.e. given any
morphism f : I ⟶ A where I is terminal, then f is an isomorphism.
Strictly speaking, this says that any terminal object must be strict, rather than that strict
terminal objects exist.
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.underEquivOfIsTerminalstatement and proof · cited by 4
- CategoryTheory.underEquivOfIsTerminalstatement and proof · cited by 4
- CategoryTheory.Limits.IsTerminal.isIso_fromstatement and proof · cited by 2
- CategoryTheory.Limits.IsTerminal.strict_hom_extstatement and proof · cited by 2
- CategoryTheory.Limits.terminal.strict_hom_extstatement and proof · cited by 1
- CategoryTheory.Limits.HasStrictTerminalObjects.outstatement and proof · cited by 1
- CategoryTheory.Limits.IsTerminal.subsingleton_tostatement and proof · cited by 1
- CategoryTheory.Limits.terminal.strict_hom_ext_iffstatement and proof · cited by 0
- CategoryTheory.Limits.terminal.subsingleton_tostatement and proof · cited by 0
- CategoryTheory.MorphismProperty.underEquivOfIsTerminal_counitIsostatement and proof · cited by 0
- CategoryTheory.MorphismProperty.underEquivOfIsTerminal_functorstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.underEquivOfIsTerminal_inversestatement and proof · cited by 0