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Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.EssentiallySmall.of_le

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P Q : CategoryTheory.ObjectProperty C}
  [CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} Q],
  P ≤ Q → CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} P
Defined in
Mathlib.CategoryTheory.ObjectProperty.Small
Cited by
3 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.ObjectProperty.EssentiallySmall
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Around this declaration

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

CategoryTheory.EssentiallySmall.of_functor · cited by 1EssentiallySmall.of_funct…CategoryTheory.ObjectProperty.isEssentiallySmall_limitsClosure · cited by 0ObjectProperty.isEssentia…AlgebraicGeometry.essentiallySmall_costructuredArrow_Spec · cited by 0AlgebraicGeometry.essenti…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryLE.le.trans · cited by 3151le.transCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…CategoryTheory.ObjectProperty.isoClosure · cited by 61ObjectProperty.isoClosureCategoryTheory.ObjectProperty.Small · cited by 30ObjectProperty.SmallCategoryTheory.ObjectProperty.EssentiallySmall · cited by 26ObjectProperty.Essentiall…CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_le' · cited by 4EssentiallySmall.exists_s…EssentiallySmall.of_leCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.