Theorems · Theorem · group theory
CategoryTheory.Subgroupoid.mul
∀ {C : Type u} [inst : CategoryTheory.Groupoid C] (self : CategoryTheory.Subgroupoid C) {c d e : C} {p : c ⟶ d},
p ∈ self.arrows c d → ∀ {q : d ⟶ e}, q ∈ self.arrows d e → CategoryTheory.CategoryStruct.comp p q ∈ self.arrows c e- Cited by
- 5 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Groupoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.arrowsstatement · cited by 53
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Subgroupoid.mem_objs_of_srcproof · cited by 4
- CategoryTheory.Subgroupoid.mem_objs_of_tgtproof · cited by 2
- CategoryTheory.Subgroupoid.id_mem_of_nonempty_isotropyproof · cited by 2
- CategoryTheory.Subgroupoid.vertexSubgroupproof · cited by 1
- CategoryTheory.Subgroupoid.mul_mem_cancel_leftproof · cited by 0
- CategoryTheory.Subgroupoid.mul_mem_cancel_rightproof · cited by 0