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In this work, we prove that\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\mathcal {C}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>C<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is a groupoid if and only if\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\mathcal {C}-\\text {set}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:mo>-<\/mml:mo>\n                            <mml:mtext>set<\/mml:mtext>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    \u00a0has finitely many indecomposable objects, which is the categorical analog of transitive\n                    <jats:italic>G<\/jats:italic>\n                    -sets in classical group actions.\n                  <\/jats:p>","DOI":"10.1007\/s10485-026-09854-2","type":"journal-article","created":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T11:37:44Z","timestamp":1775302664000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Characterization of Groupoids in Terms of Their Category of $$\\mathcal {C}$$-Sets"],"prefix":"10.1007","volume":"34","author":[{"given":"J. Miguel","family":"Calder\u00f3n","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alberto G.","family":"Raggi-C\u00e1rdenas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Itzel","family":"Rosas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ram\u00f3n H.","family":"Ruiz-Medina","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,4]]},"reference":[{"key":"9854_CR1","series-title":"Encyclopedia of Mathematics and Its Applications","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511525858","volume-title":"Handbook of Categorical Algebra","author":"F Borceux","year":"1994","unstructured":"Borceux, F.: Handbook of Categorical Algebra. Encyclopedia of Mathematics and Its Applications, vol. 1. Cambridge University Press, Cambridge (1994). https:\/\/doi.org\/10.1017\/CBO9780511525858"},{"key":"9854_CR2","doi-asserted-by":"publisher","unstructured":"Bouc, S.: Burnside rings. In: Handbook of Algebra, vol. 2, pp. 739\u2013804. North-Holland, Amsterdam (2000). https:\/\/doi.org\/10.1016\/S1570-7954(00)80043-1","DOI":"10.1016\/S1570-7954(00)80043-1"},{"key":"9854_CR3","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-11297-3","volume-title":"Biset Functors for Finite Groups","author":"S Bouc","year":"2010","unstructured":"Bouc, S.: Biset Functors for Finite Groups. Lecture Notes in Mathematics, vol. 1990. Springer, Berlin (2010)"},{"key":"9854_CR4","doi-asserted-by":"publisher","unstructured":"Dieck, T.: The Burnside ring of a finite group. J. 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