A conditon on maps between sheaves

[Andrej Bauer <andrej.bauer@andrej.com>]

Dear categorists,

I have come across a condition on maps between sheaves which I am
unable to recognize as with my feeble knowledge of sheaf theory. I
would appreciate any hints as to what this condition is about.

Succinctly but imprecisely my condition can be expressed as: the
inverse image of a sufficiently small section is again a section.

More precisely, let p : E -> B be p' : E' -> B be two etale maps over
a base space B and let f : E -> E' be a continuous map such that p = f
p'. The mystery condition on f is as follows: for every x in B there
is a neighborhood U of x, such that for every section s : U -> E' of
p' there exists a unique section t : U -> E of p for which t(U) =
f^(-1)(s(U)).

It follows from this condition that f is mono as a morphism in Sh(B)
because such an f is injective on each fiber. But I think the
condition says more than that. Am I looking at a standard notion?

With kind regards,

Andrej


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