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Banach with Eilenberg

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