{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T06:48:28Z","timestamp":1770274108998,"version":"3.49.0"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"3-4","license":[{"start":{"date-parts":[[2009,7,1]],"date-time":"2009-07-01T00:00:00Z","timestamp":1246406400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Funct. Prog."],"published-print":{"date-parts":[[2009,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Arrows are an extension of the well-established notion of a monad in functional-programming languages. This paper presents several examples and constructions and develops denotational semantics of arrows as monoids in categories of bifunctors<jats:bold>C<\/jats:bold><jats:sup>op<\/jats:sup>\u00d7<jats:bold>C<\/jats:bold>\u2192<jats:bold>C<\/jats:bold>. Observing similarities to monads \u2013 which are monoids in categories of endofunctors<jats:bold>C<\/jats:bold>\u2192<jats:bold>C<\/jats:bold>\u2013 it then considers Eilenberg\u2013Moore and Kleisli constructions for arrows. The latter yields Freyd categories, mathematically formulating the folklore claim \u2018Arrows are Freyd categories.\u2019<\/jats:p>","DOI":"10.1017\/s0956796809007308","type":"journal-article","created":{"date-parts":[[2009,6,9]],"date-time":"2009-06-09T14:05:04Z","timestamp":1244556304000},"page":"403-438","source":"Crossref","is-referenced-by-count":37,"title":["Categorical semantics for arrows"],"prefix":"10.1017","volume":"19","author":[{"given":"BART","family":"JACOBS","sequence":"first","affiliation":[]},{"given":"CHRIS","family":"HEUNEN","sequence":"additional","affiliation":[]},{"given":"ICHIRO","family":"HASUO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,7,1]]},"reference":[{"key":"S0956796809007308_ref29","first-page":"1310","article-title":"Signals and comonads","volume":"11","author":"Uustalu","year":"2005","journal-title":"J. Univ. Comput. 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