Theorems · Theorem · category theory
CategoryTheory.Limits.InitialMonoClass.of_isTerminal
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {I T : C} (hI : CategoryTheory.Limits.IsInitial I)
(hT : CategoryTheory.Limits.IsTerminal T), CategoryTheory.Mono (hI.to T) → CategoryTheory.Limits.InitialMonoClass CTo show a category is an InitialMonoClass it suffices to show the unique morphism from an
initial object to a terminal object is a monomorphism.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 32 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.
Cites11
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Limits.IsTerminal.fromproof · cited by 160
- CategoryTheory.Limits.IsInitialstatement and proof · cited by 158
- CategoryTheory.Limits.IsTerminalstatement and proof · cited by 153
- CategoryTheory.Limits.IsInitial.tostatement and proof · cited by 119
- CategoryTheory.Limits.IsInitial.hom_extproof · cited by 32
- CategoryTheory.Limits.InitialMonoClassstatement · cited by 12
- CategoryTheory.mono_of_mono_facproof · cited by 9
- CategoryTheory.Limits.InitialMonoClass.of_isInitialproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.InitialMonoClass.of_terminalproof · cited by 0