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category_of_f-algebras [2014/09/22 23:49] nikolaj |
category_of_f-algebras [2014/09/23 01:09] nikolaj |
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| The category of F-algebras and F-algebra homomorphisms. The postulate says that it can't matter if you perform the operation ($\alpha$ resp. $\beta$) before or after the transformation $f$. | The category of F-algebras and F-algebra homomorphisms. The postulate says that it can't matter if you perform the operation ($\alpha$ resp. $\beta$) before or after the transformation $f$. | ||
| - | Note that $\alpha:{\bf C}[FA,A],\beta{\bf C}[FB,B]$ were arrows in ${\bf C}$, the function $f:A\to B$ can be concatenated with those, and $\langle f\rangle$ denotes the //arrow// between $F$-algebras $\langle A,\alpha\rangle$ and $\langle B,\beta\rangle$ corresponding to the //homomorphism// $f:A\to B$. Clearly, $\langle f\rangle$ and $f$ are in bijection and one often just write $f$ for both. | + | Note that $\alpha,\beta,f$ are arrows in ${\bf C}$, while $\langle f\rangle$ denotes the arrow between $F$-algebras $\langle A,\alpha\rangle$ and $\langle B,\beta\rangle$ corresponding to the //homomorphism// $f$. Clearly, $\langle f\rangle$ and $f$ are in bijection and one often just writes $f$ for both. |
| === Reference === | === Reference === | ||
