Mathlib Map

Theorems · Definition · category theory

CategoryTheory.ObjectProperty.op

{C : Type u} →
  [inst : CategoryTheory.CategoryStruct.{v, u} C] → CategoryTheory.ObjectProperty C → CategoryTheory.ObjectProperty Cᵒᵖ

The property of objects of Cᵒᵖ corresponding to P : ObjectProperty C.

Defined in
Mathlib.CategoryTheory.ObjectProperty.Opposite
Cited by
42 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryStruct

Around this declaration

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

CategoryTheory.ObjectProperty.op_unop · cited by 10ObjectProperty.op_unopCategoryTheory.ObjectProperty.op_monotone_iff · cited by 6ObjectProperty.op_monoton…CategoryTheory.ObjectProperty.opEquivalence · cited by 5ObjectProperty.opEquivale…CategoryTheory.ObjectProperty.op_singleton · cited by 4ObjectProperty.op_singlet…CategoryTheory.ObjectProperty.isCoseparating_op_iff · cited by 3ObjectProperty.isCosepara…CategoryTheory.ObjectProperty.trW_of_op · cited by 2ObjectProperty.trW_of_opCategoryTheory.ObjectProperty.limitsOfShape_eq_unop_colimitsOfShape · cited by 2ObjectProperty.limitsOfSh…CategoryTheory.ObjectProperty.colimitsOfShape_eq_unop_limitsOfShape · cited by 2ObjectProperty.colimitsOf…CategoryTheory.ObjectProperty.isCodetecting_op_iff · cited by 2ObjectProperty.isCodetect…CategoryTheory.ObjectProperty.isDetecting_op_iff · cited by 2ObjectProperty.isDetectin…CategoryTheory.ObjectProperty.isSeparating_op_iff · cited by 2ObjectProperty.isSeparati…CategoryTheory.ObjectProperty.op_injective · cited by 2ObjectProperty.op_injecti…CategoryTheory.ObjectProperty.op_isoClosure · cited by 2ObjectProperty.op_isoClos…CategoryTheory.ObjectProperty.op_monotone · cited by 2ObjectProperty.op_monotoneCategoryTheory.ObjectProperty.op_ofObj · cited by 2ObjectProperty.op_ofObjOpposite · cited by 8081OppositeOpposite.unop · cited by 2231Opposite.unopCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…CategoryTheory.CategoryStruct · cited by 343CategoryTheory.CategorySt…ObjectProperty.opCITED BYCITES

Cites4

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

Cited by44

Results whose statement or proof uses this declaration.