Theorems · Theorem · category theory
CategoryTheory.Subobject.map_bot
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasInitial C]
[inst_2 : CategoryTheory.Limits.InitialMonoClass C] (f : X ⟶ Y) [inst_3 : CategoryTheory.Mono f],
(CategoryTheory.Subobject.map f).obj ⊥ = ⊥- Defined in
- Mathlib.CategoryTheory.Subobject.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- CategoryTheory.Functor.objstatement · cited by 19,642
- Bot.botstatement · cited by 4,720
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Limits.HasInitialstatement and proof · cited by 185
- Quotient.sound'proof · cited by 30
- CategoryTheory.Subobject.mapstatement · cited by 19
- CategoryTheory.Limits.InitialMonoClassstatement and proof · cited by 12
- CategoryTheory.MonoOver.mapBotproof · cited by 1
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