Hi, I think the following newer papers have not yet been mentioned in this discussion: - K. Asada, I. Hasuo. Categorifying computations into components via arrows as profunctors. In Proc. of 10th Wksh. on Coalgebraic Methods in Computer Science, CMCS 2010 (Paphos, March 2010), v. 264, n. 2 of Electron. Notes in Theor. Comput. Sci., Elsevier, pp. 25-45. Elsevier, 2010. http://dx.doi.org/10.1016/j.entcs.2010.07.012 - K. Asada. Arrows are strong monads. In Proc. of 3rd Wksh. on Mathematically Structured Functional Programming, MSFP 2010 Baltimore, Sept. 2010), pp. 33-41. ACM Press, 2010. These promote the view that an arrow is a strong monad in Prof (2-categorically) (building on and going further than Heunen, Jacobs, MFPS 2006, Jacobs, Hasuo, MSFP 2006, Jacobs, Heunen, Hasuo, JFP 2009.) - T. Altenkirch, J. Chapman, T. Uustalu. Monads need not be endofunctors. In L. Ong, ed., Proc. of 13th Int. Conf. on Foundations of Software Science and Computation Structures, FoSSaCS 2010 (Paphos, March 2010), v. 6014 of Lect. Notes in Comput. Sci., pp. 297-311. Springer, 2010. http://dx.doi.org/10.1007/978-3-642-12032-9_21 This paper shows that an arrow is the same as a strong "relative monad" on the Yoneda embedding. Best wishes, Tarmo U [For admin and other information see: http://www.mta.ca/~cat-dist/ ]