Library UniMath.CategoryTheory.categories.CGraph

Category of correspondence graphs

Marco Maggesi June 2019 *********************************************************************************

Precategory of precgraphs.

Category of cgraphs.

Forgetful functor.


Definition cgraph_forget_map (G : cgraph) : hSet
  := make_hSet (node G) (isaset_node G).

Definition cgraph_forget_data
  : functor_data cgraph_precategory_ob_mor hset_precategory_ob_mor
  := @make_functor_data
       cgraph_category HSET
       cgraph_forget_map
       (λ G H : cgraph, onnode).

Lemma is_functor_cgraph_forget
  : @is_functor cgraph_precategory hset_precategory cgraph_forget_data.
Show proof.
  apply make_dirprod.
  - intro x.
    cbn.
    apply idpath.
  - intros x y z. cbn.
    intros f g.
    apply idpath.

Definition cgraph_forget
  : cgraph_category HSET
  := @make_functor cgraph_precategory hset_precategory
       cgraph_forget_data
 is_functor_cgraph_forget.