Universal Quotients of Functors
by
Rolf Rother
HSM

L. Kucera showed that every category is a quotient of a concrete one [1]. V. Trnková used this to show that on each "nicely" universal concrete category A there exists an endofunctor F : A --> A and a congruence relation ~ such that F/ ~ : A/ ~ --> A/ ~ is a universal functor [2]. But neither the functor nor the congruence are naturally given.

We will see that on each "concretely" universal category there exists a (concretely) universal concrete functor F : (A, U) --> (A, U) and a congruence ~ such that F/ ~ is universal for faithful functors. The functor F we can present explicitly.

[1] L. Kucera: Every category is a factorization of a concrete one, J. Pure and Appl. Alg. 1 (1971), 373 - 376.

[2] V. Trnková: Universalities Applied Categorical Structures 2 (1994), 173 - 185.

Date received: June 6, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeq-38.