This is an archived version pinned as of the submission of my master's thesis. An up-to-date version may be found online.

The precategory of groups

module group-theory.precategory-of-groups where

open import category-theory.full-large-subprecategories
open import category-theory.large-precategories
open import category-theory.precategories

open import foundation.universe-levels

open import group-theory.groups
open import group-theory.precategory-of-semigroups

Definition

The precategory of groups as a full subprecategory of the precategory of semigroups

Group-Full-Large-Subprecategory :
  Full-Large-Subprecategory (λ l → l) Semigroup-Large-Precategory
Group-Full-Large-Subprecategory = is-group-prop-Semigroup

The large precategory of groups

Group-Large-Precategory : Large-Precategory lsuc (_⊔_)
Group-Large-Precategory =
  large-precategory-Full-Large-Subprecategory
    ( Semigroup-Large-Precategory)
    ( Group-Full-Large-Subprecategory)

The small precategories of groups

Group-Precategory : (l : Level) → Precategory (lsuc l) l
Group-Precategory = precategory-Large-Precategory Group-Large-Precategory