Banach with Eilenberg

«Sammy regarded prewar Poland with some affection. He felt that he had been well nurtured by the Polish community of mathematicians, and he told me of his pleasure on being received by Stefan Banach himself, a process of being welcomed to the holy of holies, the café in which Banach spent his time (...). Sammy’s view of Poland since the war (...) was particularly complicated by what he viewed as its treatment of category theory as a fringe subject.» — Peter Freyd, 1998, Not. Amer. Math. Soc. 45, 1350–1351.


For several hours I dreamt of Banach with Eilenberg. In this dream, Banach did not die immediately after the war, so, having read the work of Eilenberg and MacLane in 1945, he became preoccupied with the application of category theory to functional analysis, and discovered that when one considers the categories of Banach spaces, one can introduce an additional structure over them, but other than monoidal or enriched one. The development of the theory of this class of structures became a Polish speciality, but practised only by Polish émigrés in America, because in Poland itself, as a result of high social acidity, no one had enough independence, inspiration, or sheer personal courage to pursue it.


30.VIII.15, Waterloo; transl. from Polish: Brzeźno, 12.I.23