Theorems · Definition · group theory

CategoryTheory.Subgroupoid.comap

{C : Type u} →
  [inst : CategoryTheory.Groupoid C] →
    {D : Type u_1} →
      [inst_1 : CategoryTheory.Groupoid D] →
        CategoryTheory.Functor C D → CategoryTheory.Subgroupoid D → CategoryTheory.Subgroupoid C

A functor between groupoid defines a map of subgroupoids in the reverse direction by taking preimages.

Defined in: Mathlib.CategoryTheory.Groupoid.Subgroupoid
Cited by: 8 results in Mathlib
Foundations: Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Groupoid CategoryTheory.Groupoid

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

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

Quiver.Homproof · cited by 32,603
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.mapproof · cited by 8,698
Set.ofPredproof · cited by 6,101
CategoryTheory.Groupoidstatement and proof · cited by 182
CategoryTheory.Subgroupoidstatement and proof · cited by 75
CategoryTheory.Subgroupoid.arrowsproof · cited by 53

Cited by9

Results whose statement or proof uses this declaration.

CategoryTheory.Subgroupoid.galoisConnection_map_comapstatement and proof · cited by 4
CategoryTheory.Subgroupoid.kerproof · cited by 3
CategoryTheory.Subgroupoid.isNormal_comapstatement and proof · cited by 1
CategoryTheory.Subgroupoid.le_comap_mapstatement · cited by 0
CategoryTheory.Subgroupoid.map_comap_lestatement · cited by 0
CategoryTheory.Subgroupoid.map_le_iff_le_comapstatement · cited by 0
CategoryTheory.Subgroupoid.comap_compstatement · cited by 0
CategoryTheory.Subgroupoid.comap_monostatement · cited by 0
CategoryTheory.Subgroupoid.ker_compstatement · cited by 0