Instances of higher geometry in field theory

Generalisations of geometry have emerged in various forms the study field theory and quantization. This mini-review focuses on role higher three selected physical applications. After motivating describing some basic aspects algebroid structures bundles (differential graded) Q-manifolds, we briefly discuss their relation to $$(\alpha )$$ Batalin–Vilkovisky quantization topological sigma models, $$(\beta gauge theories generalized global symmetries $$(\gamma tensor theories, where universality form properties terms graded is highlighted.