Theorems · Theorem · category theory
CategoryTheory.Subobject.mk_eq_bot_iff_zero
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasZeroObject C]
[inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] {f : X ⟶ Y} [inst_3 : CategoryTheory.Mono f],
CategoryTheory.Subobject.mk f = ⊥ ↔ f = 0- Defined in
- Mathlib.CategoryTheory.Subobject.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- Bot.botstatement and proof · cited by 4,720
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Iso.transproof · cited by 566
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Limits.comp_zeroproof · cited by 365
- CategoryTheory.Subobject.mkstatement and proof · cited by 109
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.simple_of_isSimpleOrder_subobjectproof · cited by 1