This is an archived version pinned as of the submission of my master's thesis.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 commutative rings

module commutative-algebra.precategory-of-commutative-rings where

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

open import commutative-algebra.commutative-rings

open import foundation.universe-levels

open import ring-theory.precategory-of-rings

Idea

The precategory of commutative rings^¶ consists of commutative rings and homomorphisms of commutative rings.

Definitions

The precategory of commutative rings as a full subprecategory of rings

Commutative-Ring-Full-Large-Subprecategory :
  Full-Large-Subprecategory (λ l → l) Ring-Large-Precategory
Commutative-Ring-Full-Large-Subprecategory = is-commutative-prop-Ring

The large precategory of commutative rings

Commutative-Ring-Large-Precategory : Large-Precategory lsuc (_⊔_)
Commutative-Ring-Large-Precategory =
  large-precategory-Full-Large-Subprecategory
    ( Ring-Large-Precategory)
    ( Commutative-Ring-Full-Large-Subprecategory)

The precategory of commutative rings of universe level l

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