The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads Export

@article{citeulike:1534420, abstract = {Lawvere theories and monads have been the two main category theoretic formulations of universal algebra, Lawvere theories arising in 1963 and the connection with monads being established a few years later. Monads, although mathematically the less direct and less malleable formulation, rapidly gained precedence. A generation later, the definition of monad began to appear extensively in theoretical computer science in order to model computational effects, without reference to universal algebra. But since then, the relevance of universal algebra to computational effects has been recognised, leading to renewed prominence of the notion of Lawvere theory, now in a computational setting. This development has formed a major part of Gordon Plotkin's mature work, and we study its history here, in particular asking why Lawvere theories were eclipsed by monads in the 1960's, and how the renewed interest in them in a computer science setting might develop in future.}, address = {Amsterdam, The Netherlands, The Netherlands}, author = {Hyland, Martin and Power, John}, citeulike-article-id = {1534420}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=1230590}, citeulike-linkout-1 = {http://dx.doi.org/10.1016/j.entcs.2007.02.019}, citeulike-linkout-2 = {http://www.sciencedirect.com/science/article/B75H1-4N7RX2N-H/2/ac2791803ddaad079385fbacc7f7aa7a}, doi = {10.1016/j.entcs.2007.02.019}, issn = {1571-0661}, journal = {Electron. Notes Theor. Comput. Sci.}, keywords = {category\_theory, monads}, pages = {437--458}, posted-at = {2008-02-19 22:57:28}, priority = {2}, publisher = {Elsevier Science Publishers B. V.}, title = {The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads}, url = {http://dx.doi.org/10.1016/j.entcs.2007.02.019}, volume = {172}, year = {2007} }

TY - JOUR ID - citeulike:1534420 L3 - citeulike-article-id:1534420 N2 - Lawvere theories and monads have been the two main category theoretic formulations of universal algebra, Lawvere theories arising in 1963 and the connection with monads being established a few years later. Monads, although mathematically the less direct and less malleable formulation, rapidly gained precedence. A generation later, the definition of monad began to appear extensively in theoretical computer science in order to model computational effects, without reference to universal algebra. But since then, the relevance of universal algebra to computational effects has been recognised, leading to renewed prominence of the notion of Lawvere theory, now in a computational setting. This development has formed a major part of Gordon Plotkin's mature work, and we study its history here, in particular asking why Lawvere theories were eclipsed by monads in the 1960's, and how the renewed interest in them in a computer science setting might develop in future. JF - Electron. Notes Theor. Comput. Sci. SN - 1571-0661 AD - Amsterdam, The Netherlands, The Netherlands EP - 458 TI - The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads PB - Elsevier Science Publishers B. V. VL - 172 SP - 437 KW - category_theory KW - monads AU - Hyland, Martin AU - Power, John PY - 2007/// UR - http://dx.doi.org/10.1016/j.entcs.2007.02.019 ER -