In mathematics, a **symmetric obstruction theory**, introduced by Kai Behrend, is a perfect obstruction theory together with nondegenerate symmetric bilinear form.

Example: Let *f* be a regular function on a smooth variety (or stack). Then the set of critical points of *f* carries a symmetric obstruction theory in a canonical way.

Example: Let *M* be a complex symplectic manifold. Then the (scheme-theoretic) intersection of Lagrangian submanifolds of *M* carries a canonical symmetric obstruction theory.