hello there everyone zzz

$$x^i$$ $$\begin{xy} \xymatrix { {\mathscr{C}} & a \ar[r]^f \ar[dr]_{g \circ f} & b \ar[d]^g & \ar@{~>}[r]^F & & Fa \ar[r]^{Ff} \ar[dr]_*[l]{\scriptstyle F(g\circ f) = Fg\circ Ff} & Fb \ar[d]^{Fg} & {\mathscr{D}} \\ && c & \ar@{~>}[r]^F &&& Fc } \end{xy}$$

tuche!