Theorems · Theorem · category theory

CategoryTheory.Functor.mapDifferentialObject_map_f

∀ {S : Type u_1} [inst : AddMonoidWithOne S] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] [inst_3 : CategoryTheory.HasShift C S] (D : Type u')
  [inst_4 : CategoryTheory.Category.{v', u'} D] [inst_5 : CategoryTheory.Limits.HasZeroMorphisms D]
  [inst_6 : CategoryTheory.HasShift D S] (F : CategoryTheory.Functor C D)
  (η : (CategoryTheory.shiftFunctor C 1).comp F ⟶ F.comp (CategoryTheory.shiftFunctor D 1))
  (hF : ∀ (c c' : C), F.map 0 = 0) {X Y : CategoryTheory.DifferentialObject S C} (f : X ⟶ Y),
  ((CategoryTheory.Functor.mapDifferentialObject D F η hF).map f).f = F.map f.f

Defined in

Mathlib.CategoryTheory.DifferentialObject

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddMonoidWithOneCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.HasShiftCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.HasShift