Theorems · Theorem · category theory
CategoryTheory.MonoOver.initialTo_b_eq_zero
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
[inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] {B : C}, CategoryTheory.Limits.initial.to B = 0simp-normal form of bot_arrow_eq_zero.
- Defined in
- Mathlib.CategoryTheory.Subobject.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Bot.botproof · cited by 4,720
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Over.leftproof · cited by 541
- CategoryTheory.Limits.initialstatement · cited by 84
- CategoryTheory.Limits.initial.tostatement · cited by 63
- CategoryTheory.MonoOver.bot_arrow_eq_zeroproof · cited by 2
- CategoryTheory.MonoOver.bot_arrowproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.mk_eq_bot_iff_zeroproof · cited by 1
- CategoryTheory.Subobject.bot_eq_zeroproof · cited by 0
- CategoryTheory.Subobject.bot_factors_iff_zeroproof · cited by 0