module Math.FiniteCategories.NumberCategory.Examples
(
exampleNumberCategory0,
exampleNumberCategory1,
exampleNumberCategory2,
exampleNumberCategory3,
exampleNumberCategory4,
exampleNumberCategory5,
exampleDiagramOfNumberCategory,
)
where
import Math.FiniteCategories.NumberCategory
import Math.FiniteCategory
import Math.Categories.FunctorCategory
import Math.Categories.Omega
import Data.WeakSet
import Data.WeakMap
import Numeric.Natural
exampleNumberCategory0 :: NumberCategory
exampleNumberCategory0 :: NumberCategory
exampleNumberCategory0 = Natural -> NumberCategory
numberCategory Natural
0
exampleNumberCategory1 :: NumberCategory
exampleNumberCategory1 :: NumberCategory
exampleNumberCategory1 = Natural -> NumberCategory
numberCategory Natural
1
exampleNumberCategory2 :: NumberCategory
exampleNumberCategory2 :: NumberCategory
exampleNumberCategory2 = Natural -> NumberCategory
numberCategory Natural
2
exampleNumberCategory3 :: NumberCategory
exampleNumberCategory3 :: NumberCategory
exampleNumberCategory3 = Natural -> NumberCategory
numberCategory Natural
3
exampleNumberCategory4 :: NumberCategory
exampleNumberCategory4 :: NumberCategory
exampleNumberCategory4 = Natural -> NumberCategory
numberCategory Natural
4
exampleNumberCategory5:: NumberCategory
exampleNumberCategory5 :: NumberCategory
exampleNumberCategory5 = Natural -> NumberCategory
numberCategory Natural
5
exampleDiagramOfNumberCategory :: Diagram NumberCategory (IsSmallerThan Natural) Natural Omega (IsSmallerThan Natural) Natural
exampleDiagramOfNumberCategory :: Diagram
NumberCategory
(IsSmallerThan Natural)
Natural
Omega
(IsSmallerThan Natural)
Natural
exampleDiagramOfNumberCategory = Diagram
NumberCategory
(IsSmallerThan Natural)
Natural
Omega
(IsSmallerThan Natural)
Natural
diag
where
diag :: Diagram
NumberCategory
(IsSmallerThan Natural)
Natural
Omega
(IsSmallerThan Natural)
Natural
diag = Diagram{src :: NumberCategory
src = Natural -> NumberCategory
numberCategory Natural
3, tgt :: Omega
tgt = Omega
omega, omap :: Map Natural Natural
omap = (Natural -> Natural) -> Set Natural -> Map Natural Natural
forall k v. (k -> v) -> Set k -> Map k v
memorizeFunction Natural -> Natural
forall a. a -> a
id (NumberCategory -> Set Natural
forall c m o. FiniteCategory c m o => c -> Set o
ob (NumberCategory -> Set Natural) -> NumberCategory -> Set Natural
forall a b. (a -> b) -> a -> b
$ Natural -> NumberCategory
numberCategory Natural
3), mmap :: Map (IsSmallerThan Natural) (IsSmallerThan Natural)
mmap = (IsSmallerThan Natural -> IsSmallerThan Natural)
-> Set (IsSmallerThan Natural)
-> Map (IsSmallerThan Natural) (IsSmallerThan Natural)
forall k v. (k -> v) -> Set k -> Map k v
memorizeFunction IsSmallerThan Natural -> IsSmallerThan Natural
forall a. a -> a
id (NumberCategory -> Set (IsSmallerThan Natural)
forall c m o. (FiniteCategory c m o, Morphism m o) => c -> Set m
arrows (NumberCategory -> Set (IsSmallerThan Natural))
-> NumberCategory -> Set (IsSmallerThan Natural)
forall a b. (a -> b) -> a -> b
$ Natural -> NumberCategory
numberCategory Natural
3)}