The precategory of finite species

Content created by Egbert Rijke, Fredrik Bakke and Victor Blanchi.

Created on 2023-03-21.
Last modified on 2023-09-26.

module species.precategory-of-finite-species where
Imports 
open import category-theory.large-precategories

open import foundation.universe-levels

open import species.morphisms-finite-species
open import species.species-of-finite-types

Idea

The precategory of finite species consists of finite species and homomorphisms of finite species.

Definition

species-𝔽-Large-Precategory :
  (l1 : Level) →
  Large-Precategory (λ l → lsuc l1 ⊔ lsuc l) (λ l2 l3 → lsuc l1 ⊔ l2 ⊔ l3)
obj-Large-Precategory (species-𝔽-Large-Precategory l1) = species-𝔽 l1
hom-set-Large-Precategory (species-𝔽-Large-Precategory l1) = hom-set-species-𝔽
comp-hom-Large-Precategory (species-𝔽-Large-Precategory l1) {X = F} {G} {H} =
  comp-hom-species-𝔽 F G H
id-hom-Large-Precategory (species-𝔽-Large-Precategory l1) {X = F} =
  id-hom-species-𝔽 F
associative-comp-hom-Large-Precategory
  ( species-𝔽-Large-Precategory l1) {X = F} {G} {H} {K} h g f =
  associative-comp-hom-species-𝔽 F G H K h g f
left-unit-law-comp-hom-Large-Precategory
  ( species-𝔽-Large-Precategory l1) {X = F} {G} f =
  left-unit-law-comp-hom-species-𝔽 F G f
right-unit-law-comp-hom-Large-Precategory
  ( species-𝔽-Large-Precategory l1) {X = F} {G} f =
  right-unit-law-comp-hom-species-𝔽 F G f

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