Theorems · Theorem · group theory

CategoryTheory.Subgroupoid.mem_im_objs_iff

∀ {C : Type u} [inst : CategoryTheory.Groupoid C] {D : Type u_1} [inst_1 : CategoryTheory.Groupoid D]
  (φ : CategoryTheory.Functor C D) (hφ : Function.Injective φ.obj) (d : D),
  d ∈ (CategoryTheory.Subgroupoid.im φ hφ).objs ↔ ∃ c, φ.obj c = d

Defined in: Mathlib.CategoryTheory.Groupoid.Subgroupoid
Cited by: 2 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Groupoid CategoryTheory.Groupoid

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Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
Top.topproof · cited by 9,680
CategoryTheory.Groupoidstatement and proof · cited by 182
CategoryTheory.Subgroupoid.objsstatement · cited by 29
CategoryTheory.Subgroupoid.imstatement · cited by 4

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Subgroupoid.obj_surjective_of_im_eq_topproof · cited by 1
CategoryTheory.Subgroupoid.isNormal_mapproof · cited by 0