Beyond Eilenberg's Structures on Objects
by
Fred E. J. Linton
Wesleyan University, Middletown, CT USA

As described at Coimbra last summer, the category of Eilenbergian lambda-structured objects of a category A is the pullback, in Cat , of the diagram

. L^(A^op)
. |
. |
. | lambdao(-)
. |
. v
. A ---> Sets^(A^op) ,
. Yoneda

lambda: L -> Sets being any functor.

On the other hand, as described at Fribourg earlier this summer, one may start instead with a functor kappa: A -> K and consider the pullback of the diagram

. Sets^(K^op)
. |
. |
. | (-)okappa
. |
. v
. A ---> Sets^(A^op)
. Yoneda

as constituting a perfectly reasonable category of kappa-structured objects of A . [Indeed, all categories (strictly) monadic over A arise in just this way.]

The talk will speculate beyond these two observations, offering several further variations on the scheme they share in common, and combinations thereof.

Date received: August 1, 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-56.