A classical (complete) type over a set X consists of a set of formulas, potentially involving parameters from X, that can be thought of as a comprehensive description of a possible element of a model containing X. In more general contexts, where dependence on logic and formulas is to be avoided, Galois types offer an elegant alternative: the type of an element a over a model M is identified as the orbit of a under automorphisms of a very large universal model C that fix M pointwise. In recent work, I have tried to transpose Galois types and some of the associated theory and results, to model-like categories which are, nonetheless, not concrete. In particular, I have had success in the context of accessible categories with directed colimits.