Remark 97.21.5. Let $S$ be a scheme. Let $\mathcal{X}$ be a category fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. Let $A$ be an $S$-algebra. There is a notion of a short exact sequence

$(x, A_1' \to A) \to (x, A_2' \to A) \to (x, A_3' \to A)$

of deformation situations: we ask the corresponding maps between the kernels $I_ i = \mathop{\mathrm{Ker}}(A_ i' \to A)$ give a short exact sequence

$0 \to I_3 \to I_2 \to I_1 \to 0$

of $A$-modules. Note that in this case the map $A_3' \to A_1'$ factors through $A$, hence there is a canonical isomorphism $A_1' = A[I_1]$.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).