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つづき

References
5. Miller, Haynes (2000). "Leray in Oflag XVIIA: The origins of sheaf theory, sheaf cohomology, and spectral sequences" (PDF).
http://www-math.mit.edu/~hrm/papers/ss.pdf
(抜粋)
With the publication of Serre’s thesis we reach the modern era of the subject, and
Leray’s contribution to it ends (though he returned briefly to clean up some loose ends in
[51] and [52]). Despite the profound impact he had on the subject, Leray’s total output
in algebraic topology represents barely one sixth of his bibliography.
And what of sheaf theory? It was reborn in modern form in an expos´e of the 1950?
51 Cartan Seminar [13], written by Cartan and dated April 8, 1951. Following Michel
Lazard, Cartan defined a sheaf as an espace ´etal´e with group structure, and he realized
that the natural form of localization was to open sets rather than closed. The notation
Γ(F, U) was used there for the group of sections of a sheaf F over an open set U; the
order of the arguments was only reversed in later work. Cartan axiomatized the notion
of supports; Leray had used “compact supports.” Cartan defined sheaf cohomology
axiomatically, and proved existence by means of a resolution by fine sheaves. In his
1953 Brussels Colloquium paper [14] Cartan viewed a sheaf as a presheaf satisfying the
gluing conditions, though the word presheaf had to await Grothendieck. The derived
functor definition of sheaf cohomology first occurred in Grothendieck’s Kansas lectures
from 1955, exposed in 1957 in “T?ohoku,” [21].

(引用終り)