Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
f-algebra [2014/09/23 10:32]
nikolaj
f-algebra [2014/09/23 10:36]
nikolaj
Line 17: Line 17:
   * 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 $FX:=G\times X$.+  * 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 ===
Link to graph
Log In
Improvements of the human condition