Remark 115.21.2 (Construction of obstruction class). With notation as in Remark 115.21.1 let $i : U \to U'$ be a first order thickening of $U$ over $B$. Let $\mathcal{I} \subset \mathcal{O}_{U'}$ be the quasi-coherent sheaf of ideals cutting out $B$ in $B'$. The fundamental triangle

together with the map $L_{U/U'} \to \mathcal{I}[1]$ determine a map $e_{U'} : L_{U/B} \to \mathcal{I}[1]$. Combined with the map $e_\mathcal {F}$ of the previous remark we obtain

(we have also composed with the map from the derived tensor product to the usual tensor product). In other words, we obtain an element

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