License | BSD-style (see the file LICENSE) |
---|---|
Maintainer | sjoerd@w3future.com |
Stability | experimental |
Portability | non-portable |
Safe Haskell | Safe |
Language | Haskell2010 |
The (augmented) simplex category.
Simplex Category
data Simplex :: * -> * -> * where Source #
Category Simplex Source # | The (augmented) simplex category is the category of finite ordinals and order preserving maps. |
HasInitialObject Simplex Source # | The ordinal |
HasTerminalObject Simplex Source # | The ordinal |
type InitialObject Simplex Source # | |
type TerminalObject Simplex Source # | |
Functor
Functor Add Source # | Ordinal addition is a bifuntor, it concattenates the maps as it were. |
TensorProduct Add Source # | Ordinal addition makes the simplex category a monoidal category, with |
type Dom Add Source # | |
type Cod Add Source # | |
type Unit Add Source # | |
type Add :% (S m, n) Source # | |
type Add :% (Z, n) Source # | |
The universal monoid
universalMonoid :: MonoidObject Add (S Z) Source #
The maps 0 -> 1
and 2 -> 1
form a monoid, which is universal, c.f. Replicate
.