Let T be a first-order theory. A correspondence is established between internal covers of models of T and definable groupoids within T. We also consider amalgamations of independent diagrams of algebraically closed substructures, and find strong relation between covers, uniqueness for 3-amalgamation, existence of 4-amalgamation, imaginaries of T^\si, and definable groupoids. As a corollary, we describe the imaginary elements of families of finite-dimensional vector spaces over pseudo-finite fields.
"Groupoids, imaginaries and internal covers,"
Turkish Journal of Mathematics: Vol. 36:
2, Article 1.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss2/1