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expanded a bit the discussion of morphisms of sites at site
created a section Morphisms of sites -- Examples -- Injections into tangent categories.
But check.
I have tried to brush-up the entry site a bit.
rewrote the former Idea-section
gave the definition of morphism of sites in the general form (flat functors instead of left exact, since we don’t demand finite limits in the first place)
wrote out most details of the proof that a morphism of sites induces a geometric morphism of sheaf toposes over them
reorganized the Examples-section, added a subsection with “classes of examples” and one with “specific examples”.
There is plenty of room for further improvements.
flat functors instead of left exact
It is a matter of how modern we are. Your convention is that you use left exact only in the context of finitely complete categories, but many people use words flat and left exact fully interchangeably. On the other hand, I like that one considers sites which are not necessarily finitely complete.
Okay, in any case, the previous version of the entry said “finite-limit preserving functor”.
added to site more statements about the relation between morphisms of sites and geometric morphisms of their sheaf toposes
I thought of what I think is a good (or at least better than before) statement about the Idea of a site
I have added one more theorem and two more detailed proofs to site.
At site there is a strange ’reference’ (\ref{LemmaForClassifyingToposes}) that looks as if it is left over from a cut-and-paste from a latex document. Does anyone know to what it ’refers’?
I suppose what is meant is this corollary at classifying topos.
I have fixed the links.
Thanks. (I’ve just fixed a spelling typo there.)
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