Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.op_monotone_iff
∀ {C : Type u} [inst : CategoryTheory.CategoryStruct.{v, u} C] {P Q : CategoryTheory.ObjectProperty C},
P.op ≤ Q.op ↔ P ≤ Q- Cited by
- 6 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Oppositestatement · cited by 8,081
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.CategoryStructstatement and proof · cited by 343
- CategoryTheory.ObjectProperty.opstatement · cited by 42
- CategoryTheory.ObjectProperty.op_monotoneproof · cited by 2
- CategoryTheory.ObjectProperty.unop_monotoneproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_op_iff_opproof · cited by 1
- CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_iff_opproof · cited by 1
- CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_op_iff_opproof · cited by 1
- CategoryTheory.ObjectProperty.essentiallySmall_op_iffproof · cited by 1
- CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iff_opproof · cited by 1
- CategoryTheory.ObjectProperty.colimitsClosure_eq_unop_limitsClosureproof · cited by 0