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From: Ross Street <street@ics.mq.edu.au>
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Subject: Re: right adjoint by forgetting relational symbols
Date: Fri, 17 Oct 2008 09:05:06 +1100
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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. =20
Soc. (3) 20 1970 619--643.

MR0789309 (86j:13023) Joyal, Andr=E9(3-PQ)
$\delta$-anneaux et vecteurs de Witt. (French) [$\delta$-rings and =20
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 =20
> looking for
> a -R-I-G-H-T- adjoint, and by comparing the example I have and the =20
> limit
> theory axiomatizing the category of small categories (for which the =20=

> forgetful
> functor Mod(T)-->Set does not have any right adjoint since it is not
> colimit-preserving),