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Theorems · Theorem · category theory

CategoryTheory.id_nonzero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] (X : C)
  [CategoryTheory.Simple X], CategoryTheory.CategoryStruct.id X ≠ 0
Defined in
Mathlib.CategoryTheory.Simple
Cited by
3 results in Mathlib
Foundations
Depth 6 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Simple
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Around this declaration

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

CategoryTheory.isIso_iff_nonzero · cited by 3CategoryTheory.isIso_iff_…CategoryTheory.Simple.not_isZero · cited by 1Simple.not_isZeroCategoryTheory.endomorphism_simple_eq_smul_id · cited by 1CategoryTheory.endomorphi…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Simple · cited by 39CategoryTheory.SimpleCategoryTheory.Simple.mono_isIso_iff_nonzero · cited by 6Simple.mono_isIso_iff_non…CategoryTheory.id_nonzeroCITED BYCITES

Cites6

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Cited by3

Results whose statement or proof uses this declaration.