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f-algebra [2014/09/23 10:34]
nikolaj
f-algebra [2014/09/23 10:36] (current)
nikolaj
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   * 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 $FX:​=X\times X$.   * 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 $FX:​=X\times X$.
  
-  * 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.+  * Fix a monoid $M$. A monoid action ​on $X$ is a map $\alpha:M\times X\to X$, so consider $FX:=M\times X$. Incidentally, ​$\langle ​\mathbb{N},+\rangle$ can also be viewed as an $F$-algebra ​for $M=\mathbb{N}$.
  
 === Reference === === Reference ===
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