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Theorems · Definition · category theory

CategoryTheory.Subobject.botCoeIsoZero

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] → {B : C} → CategoryTheory.Subobject.underlying.obj ⊥ ≅ 0

The object underlying ⊥ : Subobject B is (up to isomorphism) the zero object.

Defined in
Mathlib.CategoryTheory.Subobject.Lattice
Cited by
2 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObject
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Subobject.bot_arrow · cited by 1Subobject.bot_arrowCategoryTheory.Limits.imageSubobject_zero · cited by 0Limits.imageSubobject_zeroCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objBot.bot · cited by 4720Bot.botCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectCategoryTheory.Iso.trans · cited by 566Iso.transCategoryTheory.Subobject · cited by 385CategoryTheory.SubobjectCategoryTheory.Subobject.underlying · cited by 211Subobject.underlyingCategoryTheory.Limits.HasZeroObject.zero' · cited by 115HasZeroObject.zero'CategoryTheory.Limits.initialIsInitial · cited by 35Limits.initialIsInitialCategoryTheory.Limits.IsInitial.uniqueUpToIso · cited by 8IsInitial.uniqueUpToIsoCategoryTheory.Limits.HasZeroObject.zeroIsInitial · cited by 5HasZeroObject.zeroIsIniti…CategoryTheory.Subobject.botCoeIsoInitial · cited by 0Subobject.botCoeIsoInitialSubobject.botCoeIsoZeroCITED BYCITES

Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.