Theorems · Definition · category theory
CategoryTheory.Limits.HasTerminal
(C : Type u₁) → [CategoryTheory.Category.{v₁, u₁} C] → PropA category has a terminal object if it has a limit over the empty diagram.
Use hasTerminal_of_unique to construct instances.
- Cited by
- 142 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 61 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- CategoryTheory.Discreteproof · cited by 2,447
- CategoryTheory.Limits.HasLimitsOfShapeproof · cited by 223
Cited by211
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.terminalstatement and proof · cited by 141
- CategoryTheory.Limits.terminal.fromstatement and proof · cited by 77
- HomotopicalAlgebra.IsFibrantstatement and proof · cited by 56
- CategoryTheory.Functor.HasRightKanExtensionproof · cited by 38
- HomotopicalAlgebra.BifibrantObjectstatement and proof · cited by 38
- HomotopicalAlgebra.bifibrantObjectsstatement and proof · cited by 37
- CategoryTheory.Limits.terminalIsTerminalstatement and proof · cited by 31
- skyscraperPresheafstatement and proof · cited by 23
- CategoryTheory.Limits.terminal.comp_fromstatement and proof · cited by 21
- HomotopicalAlgebra.FibrantObjectstatement and proof · cited by 21
- HomotopicalAlgebra.fibrantObjectsstatement and proof · cited by 20
- HomotopicalAlgebra.BifibrantObject.mkstatement and proof · cited by 15
Showing the 200 most cited of 211.