2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71160In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under flat deformations and we construct several equivalences between deformation problems.44 pagesCategory TheoryK-Theory and Homology13D10; 14A22; 18E15text