Zoran Skoda Gabriel 319

\begin{align} & S:\; o\longrightarrow A \xrightarrow{u} M \xrightarrow{v} N \longrightarrow o,\[6pt] & S’ :\; o\longrightarrow A \xrightarrow{u’} M’ \xrightarrow{v’} N’ \longrightarrow o,\[6pt] &\text{On écrira } S\preceq S’\text{ s’il existe un diagramme du type}\[6pt] &\qquad \begin{array}{c} o\longrightarrow A \xrightarrow{u} M \xrightarrow{v} N \longrightarrow o\[-1pt] \phantom{o}\Big\downarrow\scriptstyle{\id_A}\quad\quad\;\Big\downarrow\scriptstyle{m}\quad\quad\;\Big\downarrow\scriptstyle{n}\[-1pt] o\longrightarrow A \xrightarrow{u’} M’ \xrightarrow{v’} N’ \longrightarrow o \end{array}\[8pt] &\text{Diagramme commutatif utilisé :}\[6pt] &\qquad \begin{array}{c} A \xrightarrow{u’} M’\[-2pt] \scriptstyle{u}\Big\downarrow\quad\quad\Big\downarrow\scriptstyle{j_{M’}}\[-2pt] M \xrightarrow{\,j_M\,} M\Sigma_A M’ \end{array}\[8pt] &\text{et la suite }S’’=(\,o\to A \xrightarrow{j_M\circ u} M\Sigma_A M’\to \mathrm{Coker}(j_M\circ u)\to o\,) \end{align}