For my research I would like to read all the known **proofs** of the very classical result **"Coherent topoi have enough points"**, by Deligne.



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> **Ref 1**: D3.3.13 in **Sketches of an Elephant**
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provides a very logic-rooted proof of the statement, I would like to see a more *geometric* or a more *category theoretic* proof.




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Suggested by Christian Espindola



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> **Ref 2**: 7.44 in **Topos Theory** by Johnstone.
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> **Ref 3**: 9.11.3 in **Sheaves in Geometry and Logic**.
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A list of proofs of "Coherent topoi have enough points"
The proof you cite is certainly based in the completeness theorem for coherent logic, but that book contains a fully categorical proof of such a theorem, based on ideas of Joyal, so it can qualify as category-theoretic. It makes use of previous categorical constructions from other parts of the book.


For a more geometric proof you can refer to Deligne's original proof, which is actually exposed in detail in Johnstone's other book "Topos theory", section 7.4. It is actually essentially the same argument, though you can distinguish the geometric flavour here. 


And there is of course the proof given in Maclane-Moerdijk "Sheaves in geometry and logic" which is based on Barr's theorem and is also quite geometric.


