Theorems · Theorem · category theory
CategoryTheory.isSeparator_unop_iff
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (G : Cᵒᵖ),
CategoryTheory.IsSeparator (Opposite.unop G) ↔ CategoryTheory.IsCoseparator G- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Oppositestatement and proof · cited by 8,081
- Opposite.unopstatement and proof · cited by 2,231
- CategoryTheory.ObjectPropertyproof · cited by 798
- CategoryTheory.IsSeparatorstatement · cited by 58
- CategoryTheory.ObjectProperty.IsSeparatingproof · cited by 41
- CategoryTheory.IsCoseparatorstatement and proof · cited by 28
- CategoryTheory.ObjectProperty.singletonproof · cited by 20
- CategoryTheory.ObjectProperty.unop_singletonproof · cited by 4
- CategoryTheory.ObjectProperty.isSeparating_unop_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.hasCoseparator_op_iffproof · cited by 0
- CategoryTheory.Abelian.has_projective_separatorproof · cited by 0