Theorems · Theorem · category theory

CategoryTheory.Functor.shiftMap_zero

∀ {C : Type u_1} {A : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_3, u_3} A] (F : CategoryTheory.Functor C A) {M : Type u_4} [inst_2 : AddMonoid M]
  [inst_3 : CategoryTheory.HasShift C M] [inst_4 : F.ShiftSequence M]
  [inst_5 : CategoryTheory.Limits.HasZeroMorphisms C] [inst_6 : CategoryTheory.Limits.HasZeroMorphisms A]
  [F.PreservesZeroMorphisms] [∀ (n : M), (CategoryTheory.shiftFunctor C n).PreservesZeroMorphisms] (X Y : C)
  (n a a' : M) (ha' : n + a = a'), F.shiftMap 0 a a' ha' = 0

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

2 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequenceCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphisms