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Theorems · Definition · category theory

CategoryTheory.Limits.IsZero.isInitial

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X : C} → CategoryTheory.Limits.IsZero X → CategoryTheory.Limits.IsInitial X

A zero object is in particular initial.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Limits.HasZeroObject.zeroIsInitial · cited by 5HasZeroObject.zeroIsIniti…CategoryTheory.Subobject.subsingleton_of_isZero · cited by 2Subobject.subsingleton_of…CategoryTheory.Limits.IsZero.isoIsInitial · cited by 0IsZero.isoIsInitialCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.IsZero · cited by 306Limits.IsZeroCategoryTheory.Limits.IsInitial · cited by 158Limits.IsInitialCategoryTheory.Limits.IsInitial.ofUnique · cited by 0IsInitial.ofUniqueIsZero.isInitialCITED BYCITES

Cites4

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Cited by3

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