# Acerca de la Demostración en Geometría by A. I. Fetísov

By A. I. Fetísov

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For these questions Peter Hilton was well prepared, for in 1965 at the conference on categorical algebra in La Jolla he had given a talk on "Correspondences and Exact Squares", a topic which is related to pullback (cartesian) and pushout (cocartesian) squares [H73]. In trying to describe Stammbach: The work of Peter Hilton in algebra 39 the higher differentials of a spectral sequence Peter Hilton was led to consider correspondences (relations) between objects of an abelian category £ . These define a new category A .

It is Mislin: Hilton's work in topology 26 therefore necessary to modify the dual situation. Hilton and Roitberg proceeded as follows. They considered principal bundles G •> E -> S n , classified by nected Lie group. Supposing that with I E and 3 = la is defined by the pull-back diagram E Q "*• a3 The maps E D 3 IP 3 \ p and p g are the natural projections, and a* denotes the adjoint of a e TT _, (G) . Of course, 3* = &a* . One would like to show that which would imply structure in to k x G - E n x G - E o , 3 a3 a and has order a con- prime to k , one wishes to infer E where a a e TT .

0}, Let UL be any collection of Abelian groups which contains for example the collection QAr of a l l Abelian groups. Let %U'be the collection of a l l Eilenberg-MacLane spaces K(A,n) such that A e (X and n ^ 0. ) A KOJr -tower X such that 1^ i s a K(7Tn+1,n+2) for n £ 0 i s called a simple Postnikov tower and s a t i s f i e s ffn(X) - iTn. map k i s usually written k Theorem 4 (coHELP). n I t s coattaching and called a k-invariant. -tower X and l e t e :Y -*• Z be a weak X-equivalence. If p^h = ge and pgh = pf in the following diagram, then there exist g and h which make the diagram commute.