Gluing of sheaves, bundles and similar objects is the subject of descent theory. In this talk we shall focus on a kind of

noncommutative geometry where spaces are represented by Abelian categories which locally look like (= are glued from)

full categories of one sided modules over noncommutative "coordinate" rings. Locality may be in the sense

of localizations, but also more generally in the sense of faithfully flat covers presented by corings.

Principal bundles will have such global spaces with categorified action analogous to a principal action of a structure

group... more

noncommutative geometry where spaces are represented by Abelian categories which locally look like (= are glued from)

full categories of one sided modules over noncommutative "coordinate" rings. Locality may be in the sense

of localizations, but also more generally in the sense of faithfully flat covers presented by corings.

Principal bundles will have such global spaces with categorified action analogous to a principal action of a structure

group... more