Arrows, like Monads, are Monoids Export

@article{citeulike:789174, abstract = {Monads are by now well-established as programming construct in functional languages. Recently, the notion of "Arrow" was introduced by Hughes as an extension, not with one, but with two type parameters. At first, these Arrows may look somewhat arbitrary. Here we show that they are categorically fairly civilised, by showing that they correspond to monoids in suitable subcategories of bifunctors . This shows that, at a suitable level of abstraction, arrows are like monads -- which are monoids in categories of functors .Freyd categories have been introduced by Power and Robinson to model computational effects, well before Hughes' Arrows appeared. It is often claimed (informally) that Arrows are simply Freyd categories. We shall make this claim precise by showing how monoids in categories of bifunctors exactly correspond to Freyd categories.}, author = {Heunen, Chris and Jacobs, Bart}, booktitle = {Proceedings of the 22nd Annual Conference on Mathematical Foundations of Programming Semantics (MFPS XXII)}, citeulike-article-id = {789174}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.entcs.2006.04.012}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S1571066106001666}, citeulike-linkout-2 = {http://www.sciencedirect.com/science/article/B75H1-4JWBRXB-D/2/78436c00b016786f248c80eb24864f5a}, doi = {10.1016/j.entcs.2006.04.012}, journal = {Electronic Notes in Theoretical Computer Science}, keywords = {arrows, category-theory, monads}, month = {May}, pages = {219--236}, posted-at = {2006-08-08 00:22:04}, priority = {0}, title = {Arrows, like Monads, are Monoids}, url = {http://dx.doi.org/10.1016/j.entcs.2006.04.012}, volume = {158}, year = {2006} }

TY - JOUR ID - citeulike:789174 L3 - citeulike-article-id:789174 N2 - Monads are by now well-established as programming construct in functional languages. Recently, the notion of "Arrow" was introduced by Hughes as an extension, not with one, but with two type parameters. At first, these Arrows may look somewhat arbitrary. Here we show that they are categorically fairly civilised, by showing that they correspond to monoids in suitable subcategories of bifunctors . This shows that, at a suitable level of abstraction, arrows are like monads -- which are monoids in categories of functors .Freyd categories have been introduced by Power and Robinson to model computational effects, well before Hughes' Arrows appeared. It is often claimed (informally) that Arrows are simply Freyd categories. We shall make this claim precise by showing how monoids in categories of bifunctors exactly correspond to Freyd categories. JF - Electronic Notes in Theoretical Computer Science EP - 236 TI - Arrows, like Monads, are Monoids VL - 158 T2 - Proceedings of the 22nd Annual Conference on Mathematical Foundations of Programming Semantics (MFPS XXII) SP - 219 KW - arrows KW - category-theory KW - monads AU - Heunen, Chris AU - Jacobs, Bart PY - 2006/05/05/ UR - http://dx.doi.org/10.1016/j.entcs.2006.04.012 ER -