Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.singleton_iff

∀ {C : Type u} [inst : CategoryTheory.CategoryStruct.{v, u} C] (X Y : C),
  CategoryTheory.ObjectProperty.singleton X Y ↔ X = Y
Defined in
Mathlib.CategoryTheory.ObjectProperty.Basic
Cited by
4 results in Mathlib
Foundations
Depth 8 from the axioms · uses propext
Assumes
CategoryTheory.CategoryStruct
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.isCoseparator_def · cited by 5CategoryTheory.isCosepara…CategoryTheory.isSeparator_def · cited by 5CategoryTheory.isSeparato…CategoryTheory.isCodetector_def · cited by 2CategoryTheory.isCodetect…CategoryTheory.isDetector_def · cited by 2CategoryTheory.isDetector…CategoryTheory.CategoryStruct · cited by 343CategoryTheory.CategorySt…CategoryTheory.ObjectProperty.singleton · cited by 20ObjectProperty.singletonObjectProperty.singleton_iffCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.