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Theorems · Theorem · category theory

CategoryTheory.HasSubobjectClassifier.exists_classifier

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.HasSubobjectClassifier C],
  Nonempty (CategoryTheory.Subobject.Classifier C)

There is some classifier.

Defined in
Mathlib.CategoryTheory.Subobject.Classifier.Defs
Cited by
7 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.HasSubobjectClassifier
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Around this declaration

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

CategoryTheory.HasSubobjectClassifier.Ω · cited by 9HasSubobjectClassifier.ΩCategoryTheory.HasSubobjectClassifier.truth · cited by 8HasSubobjectClassifier.tr…CategoryTheory.HasSubobjectClassifier.χ · cited by 8HasSubobjectClassifier.χCategoryTheory.HasSubobjectClassifier.comm · cited by 2HasSubobjectClassifier.co…CategoryTheory.HasSubobjectClassifier.isPullback_χ · cited by 2HasSubobjectClassifier.is…CategoryTheory.HasSubobjectClassifier.unique · cited by 1HasSubobjectClassifier.un…CategoryTheory.HasSubobjectClassifier.Ω₀ · cited by 1HasSubobjectClassifier.Ω₀CategoryTheory.HasClassifier.comm · cited by 0HasClassifier.commCategoryTheory.HasClassifier.isPullback_χ · cited by 0HasClassifier.isPullback_χCategoryTheory.HasClassifier.unique · cited by 0HasClassifier.uniqueCategoryTheory.HasSubobjectClassifier.comm_assoc · cited by 0HasSubobjectClassifier.co…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Subobject.Classifier · cited by 46Subobject.ClassifierCategoryTheory.HasSubobjectClassifier · cited by 15CategoryTheory.HasSubobje…HasSubobjectClassifier.exists…CITED BYCITES

Cites3

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Cited by11

Results whose statement or proof uses this declaration.