Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.essentiallySmall_op_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty C),
CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} P.op ↔
CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} P- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.ObjectProperty.isoClosureproof · cited by 61
- CategoryTheory.ObjectProperty.opstatement and proof · cited by 42
- CategoryTheory.ObjectProperty.Smallproof · cited by 30
- CategoryTheory.ObjectProperty.unopproof · cited by 29
- CategoryTheory.ObjectProperty.EssentiallySmallstatement and proof · cited by 26
- CategoryTheory.ObjectProperty.op_unopproof · cited by 10
- CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_leproof · cited by 7
- CategoryTheory.ObjectProperty.op_monotone_iffproof · cited by 6
- CategoryTheory.ObjectProperty.op_isoClosureproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.essentiallySmall_unop_iffproof · cited by 1