Manchester Geometry Seminar 2001/2002

The notion of 2-groupoid (and, more generally, 2-category) plays an important role in pure category theory and in algebraic formulations of homotopy theory. On the other hand, the speaker has developed a substantial Lie theory for double groupoids (=groupoid objects in the category of groupoids) which is closely related to work in Poisson geometry and second-order constructions in differential geometry. This talk will make precise the relations between (Lie) 2-groupoids and double (Lie) groupoids, and between their infinitesimal invariants.