We introduce and study central types, which are generalizations of Eilenberg-Mac Lane spaces. A type is central when it is equivalent to the component of the identity among its own self-equivalences. From centrality alone we construct an infinite delooping in terms of a tensor product of banded types, which are the appropriate notion of torsor for a central type. Our constructions are carried out in homotopy type theory, and therefore hold in any $\infty$-topos. Even when interpreted into the $\infty$-topos of spaces, our main results and constructions are new. In particular, we give a description of the moduli space of H-space structures on an H-space which generalizes a formula of Arkowitz-Curjel and Copeland which counts the number of path components of this moduli space.