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Theorems · Theorem · category theory

CategoryTheory.Paths.lift_nil

∀ {V : Type u₁} [inst : Quiver V] {C : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} C] (φ : V ⥤q C) (X : V),
  (CategoryTheory.Paths.lift φ).map Quiver.Path.nil = CategoryTheory.CategoryStruct.id (φ.obj X)
Defined in
Mathlib.CategoryTheory.PathCategory.Basic
Cited by
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Foundations
Depth 15 from the axioms · uses propext
Assumes
QuiverCategoryTheory.Category
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CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idPrefunctor.obj · cited by 1241Prefunctor.objQuiver · cited by 405QuiverPrefunctor · cited by 116PrefunctorCategoryTheory.Paths · cited by 82CategoryTheory.PathsCategoryTheory.Paths.lift · cited by 7Paths.liftPaths.lift_nilCITED BYCITES

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