The precategory of commutative monoids

Content created by Egbert Rijke and Fredrik Bakke.

Created on 2023-05-06.
Last modified on 2023-11-27.

module group-theory.precategory-of-commutative-monoids where
Imports
open import category-theory.large-precategories

open import foundation.universe-levels

open import group-theory.commutative-monoids
open import group-theory.homomorphisms-commutative-monoids

Idea

The precategory of commutative monoids consists of commutative monoids and homomorphisms of monoids.

Definitions

The large precategory of commutative monoids

Commutative-Monoid-Large-Precategory : Large-Precategory lsuc _⊔_
obj-Large-Precategory
  Commutative-Monoid-Large-Precategory =
  Commutative-Monoid
hom-set-Large-Precategory
  Commutative-Monoid-Large-Precategory =
  hom-set-Commutative-Monoid
comp-hom-Large-Precategory
  Commutative-Monoid-Large-Precategory {X = K} {L} {M} =
  comp-hom-Commutative-Monoid K L M
id-hom-Large-Precategory
  Commutative-Monoid-Large-Precategory {X = M} =
  id-hom-Commutative-Monoid M
associative-comp-hom-Large-Precategory
  Commutative-Monoid-Large-Precategory {X = K} {L} {M} {N} =
  associative-comp-hom-Commutative-Monoid K L M N
inv-associative-comp-hom-Large-Precategory
  Commutative-Monoid-Large-Precategory {X = K} {L} {M} {N} =
  inv-associative-comp-hom-Commutative-Monoid K L M N
left-unit-law-comp-hom-Large-Precategory
  Commutative-Monoid-Large-Precategory {X = M} {N} =
  left-unit-law-comp-hom-Commutative-Monoid M N
right-unit-law-comp-hom-Large-Precategory
  Commutative-Monoid-Large-Precategory {X = M} {N} =
  right-unit-law-comp-hom-Commutative-Monoid M N

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