  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.
  Along the way, we further develop the theory of H-spaces in homotopy type
theory, including their relation to evaluation fibrations and Whitehead
products. These considerations let us, for example, rule out the existence of
H-space structures on the $2n$-sphere for $n > 0$. We also give a novel
description of the moduli space of H-space structures on an H-space. Using this
description, we generalize a formula of Arkowitz-Curjel and Copeland for
counting the number of path components of this moduli space. As an application,
we deduce that the moduli space of H-space structures on the $3$-sphere is
$\Omega^6 \mathbb{S}^3$.
