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We show that these two properties are in fact equivalent. In the process, we develop a general technique for associating categorical properties of a category obtained by Artin glueing with preservation properties of the functor along which the glueing takes place. We also give a syntactic characterization of those monads on Set whose functor parts have the above properties, and whose units and multiplications are cartesian natural transformations.<\/jats:p>","DOI":"10.1017\/s0960129500001183","type":"journal-article","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T09:00:09Z","timestamp":1236157209000},"page":"441-459","source":"Crossref","is-referenced-by-count":59,"title":["Connected limits, familial representability and Artin glueing"],"prefix":"10.1017","volume":"5","author":[{"given":"Aurelio","family":"Carboni","sequence":"first","affiliation":[]},{"given":"Peter","family":"Johnstone","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,4]]},"reference":[{"key":"S0960129500001183_ref018","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-53982-4_13"},{"key":"S0960129500001183_ref022","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9839-7"},{"key":"S0960129500001183_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(92)90048-K"},{"key":"S0960129500001183_ref005","unstructured":"Diers Y. 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