Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.IsCoseparating.mono_productTo
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.ObjectProperty C},
P.IsCoseparating →
∀ (X : C) [inst_1 : CategoryTheory.Limits.HasProduct (P.productToFamily X)], CategoryTheory.Mono (P.productTo X)- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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.Category.assocproof · cited by 6,433
- CategoryTheory.Monostatement · cited by 893
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
- CategoryTheory.StructuredArrowstatement and proof · cited by 370
- CategoryTheory.Limits.limit.lift_πproof · cited by 266
- CategoryTheory.Limits.piObjstatement · cited by 237
- CategoryTheory.StructuredArrow.homproof · cited by 150
- CategoryTheory.StructuredArrow.mkproof · cited by 125
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.hasInitial_of_isCoseparatingproof · cited by 2
- CategoryTheory.ObjectProperty.isCoseparating_iff_monoproof · cited by 0