Portability | non-portable |
---|---|
Stability | experimental |
Maintainer | sjoerd@w3future.com |
Safe Haskell | Safe-Inferred |
The (augmented) simplex category.
Simplex Category
Category Simplex | The (augmented) simplex category is the category of finite ordinals and order preserving maps. |
HasBinaryCoproducts Simplex | The coproduct in the simplex category is a merge operation. |
HasInitialObject Simplex | The ordinal |
HasTerminalObject Simplex | The ordinal |
Functor
Functor Add | Ordinal addition is a bifuntor, it concattenates the maps as it were. |
TensorProduct Add | Ordinal addition makes the simplex category a monoidal category, with |
The universal monoid
universalMonoid :: MonoidObject (CoproductFunctor Simplex) (S Z)Source
The maps 0 -> 1
and 2 -> 1
form a monoid, which is universal, c.f. Replicate
.
Replicate f (MonoidObject f a) |
TensorProduct f => Functor (Replicate f a) | Replicate a monoid a number of times. |