category_of_f-algebras

Category of F-algebras

Collection

context	$F$ in ${\bf C}\longrightarrow{\bf C}$
definiendum	$\mathcal{A}:\mathrm{Ob}_\mathrm{it}$
postulate	$\mathcal{A}$ … $F$ -algebra
definiendum	$\langle f\rangle:\mathrm{it}[\langle A,\alpha\rangle, \langle B,\beta\rangle]$
postulate	$f\circ\alpha=\beta\circ F(f)$

Discussion

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 $\alpha,\beta,f$ 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.

Category of F-algebras

Collection

Discussion

Reference

Parents

Context*

Requirements

Element of