A First Course in Topos Quantum Theory by Cecilia Flori

Author:Cecilia Flori
Language: eng
Format: epub, pdf
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(14.22)

By the sheaf condition, this implies s x =s y on W x ∩W y . We thus obtain a family of elements s x ∈P(W x ) such that they agree on the two maps ∏ x∈U P(W x )⇉∏ y,x∈U P(W x ∩W y ). From the condition of being a sheaf it follows that there exists an s∈P(U) such that . Then at each x∈U we have . Therefore . □

It follows that all sheaves are sheaves of cross sections of some bundle.

Moreover it is possible to generalise the above process and define a pair of functors

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