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Theorems · Definition · category theory

CategoryTheory.HasSubobjectClassifier.truthIsRegularMono

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.HasSubobjectClassifier C] →
      CategoryTheory.RegularMono (CategoryTheory.HasSubobjectClassifier.truth C)

truth C is a regular monomorphism (because it is split).

Defined in
Mathlib.CategoryTheory.Subobject.Classifier.Defs
Cited by
0 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.HasSubobjectClassifier
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Around this declaration

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

CategoryTheory.HasClassifier.truthIsRegularMono · cited by 0HasClassifier.truthIsRegu…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.HasSubobjectClassifier · cited by 15CategoryTheory.HasSubobje…CategoryTheory.RegularMono · cited by 14CategoryTheory.RegularMonoCategoryTheory.HasSubobjectClassifier.Ω · cited by 9HasSubobjectClassifier.ΩCategoryTheory.HasSubobjectClassifier.truth · cited by 8HasSubobjectClassifier.tr…CategoryTheory.HasSubobjectClassifier.Ω₀ · cited by 1HasSubobjectClassifier.Ω₀CategoryTheory.RegularMono.ofIsSplitMono · cited by 0RegularMono.ofIsSplitMonoHasSubobjectClassifier.truthI…CITED BYCITES

Cites7

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Cited by1

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