  Categories of models of algebraic theories have good categorical properties
except for gluing. Building upon insights and examples from Synthetic
Differential Geometry, we introduce a generalisation of models of algebraic
theories to infinitesimal models. We demonstrate that the category of
infinitesimal models retains most of the good categorical properties, but with
a stark improvement in the behaviour of gluing. This makes infinitesimal models
an interesting natural construction with the ability to interpolate between
algebra and geometry.
