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\DeclareMathOperator{\codim}{codim} \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\Ext}{Ext} \DeclareMathOperator{\TropB}{TropB} \DeclareMathOperator{\weight}{wt} \DeclareMathOperator{\Span}{span} \DeclareMathOperator{\Coh}{Coh} \DeclareMathOperator{\Pic}{Pic} \DeclareMathOperator{\Fuk}{Fuk} \DeclareMathOperator{\str}{star} \DeclareMathOperator{\Ob}{Ob} \DeclareMathOperator{\Coh}{Coh} \DeclareMathOperator{\CritVal}{CritV} \DeclareMathOperator{\Sing}{Sing} \DeclareMathOperator{\FS}{FS} \DeclareMathOperator{\Vect}{Vect} \DeclareMathOperator{\grad}{grad} \DeclareMathOperator{\Supp}{Supp} \DeclareMathOperator{\Bl}{Bl} \DeclareMathOperator{\Spec}{Spec} \DeclareMathOperator{\Tw}{Tw} \DeclareMathOperator{\Int}{Int} \DeclareMathOperator{\Arg}{\mathbf{M}}\begin{filecontents}{references.bib} @article{ballard2012hochschild, title={Hochschild dimensions of tilting objects}, author={Ballard, Matthew and Favero, David}, journal={International Mathematics Research Notices}, volume={2012}, 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Let $L_0, \ldots L_k\in \Fuk(X)$ be Lagrangian submanifolds, and suppose there exists a monotone Lagrangian cobordism $K: (L_0, \ldots, L_k)\rightsquigarrow \emptyset$. Then there exists an iterated cone decomposition in $\text{mod}-\Fuk(X)$, \[ \begin{tikzpicture} \node (v1) at (1.5,-0.5) {$C_0$}; \node (v2) at (3,-0.5) {$C_1$}; \node (v3) at (4.5,-0.5) {$C_2$}; \node (v4) at (6,-0.5) {$C_3$}; \node (v6) at (8,-0.5) {$C_{k-1}$}; \node (v7) at (9.5,-0.5) {$C_k$}; \node (v8) at (1.5,-2) {$L_0$}; \node (v9) at (3,-2) {$L_1$}; \node (v10) at (4.5,-2) {$L_2$}; \node (v11) at (8,-2) {$L_{k-1}$}; \node (v5) at (7,-0.5) {$\cdots$}; \draw[->] (v1) edge (v2); \draw[->] (v2) edge (v3); \draw[->] (v3) edge (v4); \draw[->] (v4) edge (v5); \draw[->] (v5) edge (v6); \draw[->] (v6) edge (v7); \draw[->] (v8) edge (v1); \draw[->] (v9) edge (v2); \draw[->] (v10) edge (v3); \draw[->] (v11) edge (v6); \draw[->,dashed] (v2) edge node[fill=white]{$[1]$} (v8); \draw[->,dashed] (v3) edge node[fill=white]{$[1]$} (v9); \draw[->,dashed] (v4) edge node[fill=white]{$[1]$} (v10); \draw[->,dashed] (v7) edge node[fill=white]{$[1]$} (v11); \end{tikzpicture}\]where each triangle in the diagram an exact triangle, $C_0=0$, and $C_k=k$. \end{theorem} \printbibliography \end{document}