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f-algebra [2014/09/22 23:21] nikolaj |
f-algebra [2014/09/23 10:34] nikolaj |
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| === Example === | === Example === | ||
| - | Addition of natural numbers is a binary relation: | + | The following examples assume that ${\bf C}$ contains all the relevant ingredients (e.g. products). |
| - | $+:\mathbb{N}\times\mathbb{N}\to\mathbb{N}.$ | + | * 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 $FX:=X\times X$. |
| - | Hence $\langle \mathbb{N},+\rangle$ is an $F$-algebra for the endofunctor with object map $FX:=X\times X$. | + | * Group actions on $X$ are maps $m:G\times X\to X$, so consider $F_GX:=G\times X$. The first example is also an $F_\mathbb{N}$-algebra. |
| === Reference === | === Reference === | ||
