Theorems · Theorem · group theory
CategoryTheory.Subgroupoid.mul_mem_cancel_left
∀ {C : Type u} [inst : CategoryTheory.Groupoid C] (S : CategoryTheory.Subgroupoid C) {c d e : C} {f : c ⟶ d}
{g : d ⟶ e}, f ∈ S.arrows c d → (CategoryTheory.CategoryStruct.comp f g ∈ S.arrows c e ↔ g ∈ S.arrows d e)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Groupoid
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.arrowsstatement and proof · cited by 53
- CategoryTheory.IsIso.inv_hom_id_assocproof · cited by 37
- CategoryTheory.Groupoid.invproof · cited by 36
- CategoryTheory.Groupoid.inv_eq_invproof · cited by 15
- CategoryTheory.Subgroupoid.invproof · cited by 6
- CategoryTheory.Subgroupoid.mulproof · cited by 5
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