INFINITY SHEAVES

This article requires as prerequisites an article about the formalization of the category theory and topos theory: Formal Set Topos.

INTRO

The concept of a sheaf was conceived in the German camp for prisoners of war called Oflag XVII where French officers taken captive during the fighting in France in the spring 1940 were imprisoned. Among them was the mathematician and lieutenant Jean Leray. In the camp he gave a course in algebraic topology during which he introduced some version of the theory of sheaves.

Jean Leray was aimed at calculating the cohomology of a total space of a fibration in terms of invariants of the base and the fibres (and naturally the fibration). To achieve this in addition to the concept of sheaves, he invented spectral sequences.

After the war Henri Cartan and Jean Pierre Serre developed the theory further, and finally the theory was brought to the state as we know it today by Alexandre Grothendieck.