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Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.nonempty_of_prop

∀ {C : Type u} [inst : CategoryTheory.CategoryStruct.{v, u} C] {P : CategoryTheory.ObjectProperty C} {X : C},
  P X → P.Nonempty
Defined in
Mathlib.CategoryTheory.ObjectProperty.Basic
Cited by
5 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryStruct
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Around this declaration

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

CategoryTheory.MorphismProperty.nonempty_cokernels · cited by 0MorphismProperty.nonempty…CategoryTheory.MorphismProperty.nonempty_kernels · cited by 0MorphismProperty.nonempty…CategoryTheory.ObjectProperty.nonempty_iSup · cited by 0ObjectProperty.nonempty_i…CategoryTheory.ObjectProperty.nonempty_of_lt · cited by 0ObjectProperty.nonempty_o…CategoryTheory.ObjectProperty.Nonempty.mono · cited by 0Nonempty.monoCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…CategoryTheory.CategoryStruct · cited by 343CategoryTheory.CategorySt…CategoryTheory.ObjectProperty.Nonempty · cited by 13ObjectProperty.NonemptyObjectProperty.nonempty_of_pr…CITED BYCITES

Cites3

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Cited by5

Results whose statement or proof uses this declaration.