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Theorems · Theorem · category theory

CategoryTheory.Limits.zero_of_source_iso_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C} (f : X ⟶ Y) (i : X ≅ 0), f = 0
Defined in
Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms
Cited by
7 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.MonoOver.bot_arrow_eq_zero · cited by 2MonoOver.bot_arrow_eq_zeroCategoryTheory.Subobject.bot_arrow · cited by 1Subobject.bot_arrowCategoryTheory.Limits.isIso_of_source_target_iso_zero · cited by 1Limits.isIso_of_source_ta…CategoryTheory.Preadditive.mono_of_kernel_iso_zero · cited by 0Preadditive.mono_of_kerne…CategoryTheory.Limits.zero_of_source_iso_zero' · cited by 0Limits.zero_of_source_iso…CategoryTheory.Limits.kernel.ι_of_mono · cited by 0kernel.ι_of_monoCategoryTheory.Limits.epi_of_target_iso_zero · cited by 0Limits.epi_of_target_iso_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Category.id_comp · cited by 1998Category.id_compCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectCategoryTheory.Limits.comp_zero · cited by 365Limits.comp_zeroCategoryTheory.Limits.zero_comp · cited by 339Limits.zero_compCategoryTheory.Iso.hom_inv_id_assoc · cited by 187Iso.hom_inv_id_assocCategoryTheory.Limits.HasZeroObject.zero' · cited by 115HasZeroObject.zero'CategoryTheory.Limits.id_zero · cited by 7Limits.id_zeroLimits.zero_of_source_iso_zeroCITED BYCITES

Cites15

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Cited by7

Results whose statement or proof uses this declaration.