Angel "Java" Lopez en Blog

Publicado el 18 de Febrero, 2018, 14:00

En 1945 se publica el "paper" seminal de toda la teoría de categorías, el "General theory of natural equivalences", de Eilenberg y McLane. Ambos autores habían comenzado a colaborar apenas unos años antes. Leo en "Tool and Object, A History and Philosophy of Category Theory" de Ralf Krömer, en el capítulo 2:

Around the beginning of the 1940s, Samuel Eilenberg and Saunders Mac Lane were working in (at first glance) very different domains: Eilenberg was interested in questions of algebraic topology, Mac Lane in algebraic number theory. The impulse for their collaboration was the observation of unexpected overlappings of both domains. (And it is a "slogan" of later CT that quite different domains may be related in an unexpected manner.)

Eilenberg estaba investigando solenoides, que son espacios topológicos con algunas características especiales. McLane se dedicaba entonces al estudio de la extensión de grupos. En el libro de arriba, se cita a Eilenberg, 1993, "Karol Borsuk—personal reminiscences.” Topol. Methods Nonlinear
Anal. 1:

When Saunders Mac Lane lectured in 1940 at the University of Michigan on group extensions one of the groups appearing on the blackboard was exactly the group calculated by Steenrod [H1(S3 Σ, Z)]. I recognized it and spoke about it to Mac Lane. The result was the joint paper...

Ese "paper" es de 1942, "Group extensions and homology", al que le seguiría en ese mismo año el "Natural isomorphisms in group theory". Pero la gran relación que apareció fue entre homología en topología y las extensiones de grupo.

Por su parte, McLane escribe en 1989, “The development of mathematical ideas by collision: the case of categories and topos theory.” En Categorical topology and its relation to analysis, algebra and combinatorics

[Mac Lane] had calculated a particular case [of Ext(G,A)] which seemed of interest: That in which G is the abelian group generated by the list of elements an, where an+1 = pan for a prime p. After a lecture by Mac Lane on this calculation, Eilenberg pointed out that the calculation closely esembled that for the regular cycles of the p-adic solenoid [ . . . ]

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Angel "Java" Lopez