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Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.op_singleton

∀ {C : Type u} [inst : CategoryTheory.CategoryStruct.{v, u} C] (X : C),
  (CategoryTheory.ObjectProperty.singleton X).op = CategoryTheory.ObjectProperty.singleton (Opposite.op X)
Defined in
Mathlib.CategoryTheory.ObjectProperty.Opposite
Cited by
4 results in Mathlib
Foundations
Depth 9 from the axioms · uses propext, Quot.sound
Assumes
CategoryTheory.CategoryStruct
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.isSeparator_op_iff · cited by 2CategoryTheory.isSeparato…CategoryTheory.isDetector_op_iff · cited by 1CategoryTheory.isDetector…CategoryTheory.isCodetector_op_iff · cited by 1CategoryTheory.isCodetect…CategoryTheory.isCoseparator_op_iff · cited by 1CategoryTheory.isCosepara…Opposite · cited by 8081OppositeCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…CategoryTheory.CategoryStruct · cited by 343CategoryTheory.CategorySt…CategoryTheory.ObjectProperty.op · cited by 42ObjectProperty.opCategoryTheory.ObjectProperty.ofObj · cited by 37ObjectProperty.ofObjCategoryTheory.ObjectProperty.singleton · cited by 20ObjectProperty.singletonCategoryTheory.ObjectProperty.op_ofObj · cited by 2ObjectProperty.op_ofObjObjectProperty.op_singletonCITED BYCITES

Cites7

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.