Right adjoints to algebraic functors are very interesting. Witt vectors and lambda-rings are key words. See MR0265348 (42 #258) Tall, D. O.; Wraith, G. C. Representable functors and operations on rings. Proc. London Math. Soc. (3) 20 1970 619--643. MR0789309 (86j:13023) Joyal, André(3-PQ) $\delta$-anneaux et vecteurs de Witt. (French) [$\delta$-rings and Witt vectors] C. R. Math. Rep. Acad. Sci. Canada 7 (1985), no. 3, 177--182. May not be relevant to your examples! Regards, Ross On 16/10/2008, at 9:19 PM, Gaucher Philippe wrote:
Thank you for all answers. But they do not give what I want. I am looking for a -R-I-G-H-T- adjoint, and by comparing the example I have and the limit theory axiomatizing the category of small categories (for which the forgetful functor Mod(T)-->Set does not have any right adjoint since it is not colimit-preserving),