Theorems · Theorem · category theory
CategoryTheory.Subobject.Classifier.truth_comp_hom_assoc
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {𝒞₁ 𝒞₂ : CategoryTheory.Subobject.Classifier C} {Z : C}
(h : 𝒞₂.Ω ⟶ Z),
CategoryTheory.CategoryStruct.comp 𝒞₁.truth (CategoryTheory.CategoryStruct.comp (𝒞₁.hom 𝒞₂) h) =
CategoryTheory.CategoryStruct.comp (𝒞₂.χ₀ 𝒞₁.Ω₀) (CategoryTheory.CategoryStruct.comp 𝒞₂.truth h)- Cited by
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- Foundations
- Depth 7 from the axioms · uses Quot.sound
- Assumes
- CategoryTheory.Category
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Cites11
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Subobject.Classifierstatement and proof · cited by 46
- CategoryTheory.Subobject.Classifier.Ωstatement and proof · cited by 33
- CategoryTheory.Subobject.Classifier.Ω₀statement and proof · cited by 26
- CategoryTheory.Subobject.Classifier.truthstatement and proof · cited by 19
- CategoryTheory.Subobject.Classifier.χ₀statement and proof · cited by 19
- CategoryTheory.Subobject.Classifier.homstatement and proof · cited by 13
- CategoryTheory.Subobject.Classifier.truth_comp_homproof · cited by 2
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