We introduce homotopy reflection structures in (∞,2)-categories, equipped with a homotopy coherent involutive endofunctor and associated difference data defined at the level of mapping spaces. We define reflection obstruction classes arising from nontrivial elements in the fundamental group of mapping spaces and study their behavior under homotopy coherent functors into locally discrete (∞,2)-categories. Our main result shows that all reflection obstruction classes are annihilated under any such functor, demonstrating a fundamental incompatibility between reflection-based homotopy data and discrete categorical realizations. This provides a homotopy-theoretic obstruction to the faithful realization of reflection structures under truncation and can be interpreted as a failure of preservation of higher coherence data.
Yugo Hidaka (Thu,) studied this question.