I am studying Riemann-Roch theorem on the book by Stitchtenoth, "Algebraic function fields and codes".
I am having some troubles understanding a exact sequence of linear mappings between Riemann-Roch spaces and adeles (pag. 25).
Let $F/K$ be a function field. Let $A_1,A_2$ two divisors on $F$ such that $A_1\leq A_2$. We then have the sequence of linear mappings $$ 0 \to \mathscr{L}(A_2)/\mathscr{L}(A_1) \xrightarrow{\sigma_1} \mathcal{A}_F(A_2)/\mathcal{A}_F(A_1) \xrightarrow{\sigma_2} (\mathcal{A}_F(A_2)+F)/(\mathcal{A}_F(A_1)+F) \to 0. $$
The book says it is defined in the obvoius manner, but which is the obvious manner of defining this linear maps $\sigma_1$ and $\sigma_2 $?