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F-algebra
Collection
| context | $F$ in ${\bf C}\longrightarrow{\bf C}$ |
| definiendum | $\langle A,\alpha\rangle$ in $\text{it}$ |
| postulate | $\alpha:{\bf C}[FA,A]$ |
Discussion
Think types $\mathrm{a}$ and $\alpha$'s of type
type Algebra f a = f a -> a
Example
Addition of natural numbers is a binary relation:
$+:\mathbb{N}\times\mathbb{N}\to\mathbb{N}.$
Hence $\langle \mathbb{N},+\rangle$ is an $F$-algebra for the endofunctor with object map $FX:=X\times X$.
Reference
Wikipedia: F-algbera
Parents
Context
