Theorems · Theorem · category theory
CategoryTheory.Subobject.Classifier.hom_comp_hom
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (𝒞₁ 𝒞₂ 𝒞₃ : CategoryTheory.Subobject.Classifier C),
CategoryTheory.CategoryStruct.comp (𝒞₁.hom 𝒞₂) (𝒞₂.hom 𝒞₃) = 𝒞₁.hom 𝒞₃- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Subobject.Classifierstatement and proof · cited by 46
- CategoryTheory.Subobject.Classifier.Ωstatement · cited by 33
- CategoryTheory.Subobject.Classifier.truthproof · cited by 19
- CategoryTheory.IsPullback.paste_vertproof · cited by 19
- CategoryTheory.Subobject.Classifier.homstatement · cited by 13
- CategoryTheory.Subobject.Classifier.uniqproof · cited by 6
- CategoryTheory.Subobject.Classifier.isPullbackproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Classifier.hom_comp_homproof · cited by 0
- CategoryTheory.Subobject.Classifier.hom_comp_hom_assocproof · cited by 0