Remark 98.21.5. 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].
Comments (0)