A categorical approach to internality
Published in Models, logics, and higher-dimensional categories, 2011
Recommended citation: Kamensky, M. A categorical approach to internality. In B. Hart, T. G. Kucera, A. Pillay, P. J. Scott, & R. A. G. Seely (Eds.), Models, logics, and higher-dimensional categories (Vol. 53, pp. 139–156). American Mathematical Society. https://arxiv.org/abs/1012.3185
Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an analogous result on the categorical level. The model theoretic statement is recovered by considering the category of definable sets.