Theorems · Definition · group theory

CategoryTheory.Subgroupoid.im

{C : Type u} →
  [inst : CategoryTheory.Groupoid C] →
    {D : Type u_1} →
      [inst_1 : CategoryTheory.Groupoid D] →
        (φ : CategoryTheory.Functor C D) → Function.Injective φ.obj → CategoryTheory.Subgroupoid D

The image of a functor injective on objects

Defined in: Mathlib.CategoryTheory.Groupoid.Subgroupoid
Cited by: 4 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Groupoid CategoryTheory.Groupoid

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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.

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.Subgroupoidstatement · cited by 75
CategoryTheory.Subgroupoid.mapproof · cited by 10

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Subgroupoid.mem_im_objs_iffstatement · cited by 2
CategoryTheory.Subgroupoid.mem_im_iffstatement and proof · cited by 1
CategoryTheory.Subgroupoid.obj_surjective_of_im_eq_topstatement and proof · cited by 1
CategoryTheory.Subgroupoid.isNormal_mapstatement and proof · cited by 0