  We formulate and prove a twofold generalisation of Lie's second theorem that
integrates homomorphisms between formal group laws to homomorphisms between Lie
groups. Firstly we generalise classical Lie theory by replacing groups with
categories. Secondly we include categories whose underlying spaces are not
smooth manifolds. The main intended application is when we replace the category
of smooth manifolds with a well-adapted model of synthetic differential
geometry. In addition we provide an axiomatic system that specifies the
abstract structures that are required to prove Lie's second theorem. As a part
of this abstract structure we define the notion of enriched mono-coreflective
subcategory which makes precise the notion of a subcategory of local models.
