{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:34:33Z","timestamp":1777646073982,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[1997,1,1]],"date-time":"1997-01-01T00:00:00Z","timestamp":852076800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[1997,9]]},"abstract":"<jats:p>This paper introduces the notion of the kernel of a relational morphism of categories. This is the second step in the working out of a useful definition of the block product of two C-varieties which in turn is needed for the theory of decompositions of monoids by means of wreath or block products. In a previous work, the author defined the construction of the block product of two categories and the strong semidirect product functor. In this second part, we construct a left adjoint of the strong semidirect product functor which is the starting point of our construction of the kernel of a relational morphism. With these notions we define the block product of two C-varieties and prove a kernel theorem in the category settings which extends a work of J. Rhodes and B. Tilson.<\/jats:p>","DOI":"10.3233\/fi-1997-313410","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T21:16:57Z","timestamp":1575321417000},"page":"401-421","source":"Crossref","is-referenced-by-count":2,"title":["The Kernel of a Relational Morphism of Categories"],"prefix":"10.1177","volume":"31","author":[{"given":"Jean-Fran\u00e7ois","family":"Rey","sequence":"first","affiliation":[{"name":"Institut Gaspard Monge, Universit\u00e9 de Marne la Vall\u00e9e., 2, rue de la Butte Verte. 93166 Noisy le Grand Cedex France. e-mail: jfrey@monge.univ-mlv.fr"}]}],"member":"179","published-online":{"date-parts":[[1997,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-1997-313410","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-1997-313410","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:34:12Z","timestamp":1777444452000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-1997-313410"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1,1]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[1997,9]]}},"alternative-id":["10.3233\/FI-1997-313410"],"URL":"https:\/\/doi.org\/10.3233\/fi-1997-313410","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1,1]]}}}