Coalgebra Bundles

We develop a generalised theory of bundles and connections on them in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory, embeddable quantum homogeneous spaces and braided group gauge theory, the latter being introduced now by these means. Examples include ones in which the gauge groups are the braided line and the quantum plane. Received: 22 February 1996 / Accepted: 29 May 1997