Linear Representations and Frobenius Morphisms of Groupoids Barbarán Sánchez, Juan Jesús El Kaoutit Zerri, Laiachi Linear representations of groupoids Inductions and co-induction functors Translation groupoids Frobenius extensions Frobenius reciprocity formula Restriction Groupoids-bisets Given a morphism of (small) groupoids with injective object map, we provide su cient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A morphism with this property is termed a Frobenius morphism of groupoids. As a consequence, an extension by a subgroupoid is Frobenius if and only if each bre of the (left or right) pull-back biset has nitely many orbits. Our results extend and clarify the classical Frobenius reciprocity formulae in the theory of nite groups, and characterize Frobenius extension of algebras with enough orthogonal idempotents. 2020-01-22T12:05:10Z 2020-01-22T12:05:10Z 2019-03-12 journal article Juan Jesús Barbarán Sánchez, Laiachi El Kaoutit, “Linear Representations and Frobenius Morphisms of Groupoids”, SIGMA, 15 (2019), 019, 33 pp. http://hdl.handle.net/10481/59015 10.3842/SIGMA.2019.019 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access Atribución-NoComercial-SinDerivadas 3.0 España Steklov Mathematical Institute RAS