A list of proofs of “Coherent topoi have enough points”Set-theoretic forcing over sites?What do coherent topoi have to do with completeness?Is it possible for a theorem to be constructive only in a non-constructive metatheory?The real numbers object in Sh(Top)Can the algebraic geometry of schemes be developed internally in topoi?Model existence theorem in topos theoryWhat is the geometric significance of fibered category theory in topos theory?
A list of proofs of “Coherent topoi have enough points”
Set-theoretic forcing over sites?What do coherent topoi have to do with completeness?Is it possible for a theorem to be constructive only in a non-constructive metatheory?The real numbers object in Sh(Top)Can the algebraic geometry of schemes be developed internally in topoi?Model existence theorem in topos theoryWhat is the geometric significance of fibered category theory in topos theory?
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For my research I would like to read all the known proofs of the very classical result "Coherent topoi have enough points", by Deligne.
Ref 1: D3.3.13 in Sketches of an Elephant
provides a very logic-rooted proof of the statement, I would like to see a more geometric or a more category theoretic proof.
Suggested by Christian Espindola
Ref 2: 7.44 in Topos Theory by Johnstone.
Ref 3: 9.11.3 in Sheaves in Geometry and Logic.
reference-request ct.category-theory topos-theory
asked 8 hours ago
Ivan Di LibertiIvan Di Liberti
2,0091 gold badge7 silver badges23 bronze badges
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add a comment |
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For my research I would like to read all the known proofs of the very classical result "Coherent topoi have enough points", by Deligne.
Ref 1: D3.3.13 in Sketches of an Elephant
provides a very logic-rooted proof of the statement, I would like to see a more geometric or a more category theoretic proof.
Suggested by Christian Espindola
Ref 2: 7.44 in Topos Theory by Johnstone.
Ref 3: 9.11.3 in Sheaves in Geometry and Logic.
reference-request ct.category-theory topos-theory
asked 8 hours ago
Ivan Di LibertiIvan Di Liberti
2,0091 gold badge7 silver badges23 bronze badges
$endgroup$
3
$begingroup$
The original proof by Deligne appeared in SGA4, but it might be a little bit hard to found: it is in the appendix of exposé VI, (which is part II)
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– Simon Henry
8 hours ago
add a comment |
$begingroup$
For my research I would like to read all the known proofs of the very classical result "Coherent topoi have enough points", by Deligne.
Ref 1: D3.3.13 in Sketches of an Elephant
provides a very logic-rooted proof of the statement, I would like to see a more geometric or a more category theoretic proof.
Suggested by Christian Espindola
Ref 2: 7.44 in Topos Theory by Johnstone.
Ref 3: 9.11.3 in Sheaves in Geometry and Logic.
reference-request ct.category-theory topos-theory
asked 8 hours ago
Ivan Di LibertiIvan Di Liberti
2,0091 gold badge7 silver badges23 bronze badges
$endgroup$
For my research I would like to read all the known proofs of the very classical result "Coherent topoi have enough points", by Deligne.
Ref 1: D3.3.13 in Sketches of an Elephant
provides a very logic-rooted proof of the statement, I would like to see a more geometric or a more category theoretic proof.
Suggested by Christian Espindola
Ref 2: 7.44 in Topos Theory by Johnstone.
Ref 3: 9.11.3 in Sheaves in Geometry and Logic.
reference-request ct.category-theory topos-theory
reference-request ct.category-theory topos-theory
asked 8 hours ago
Ivan Di LibertiIvan Di Liberti
2,0091 gold badge7 silver badges23 bronze badges
asked 8 hours ago
Ivan Di LibertiIvan Di Liberti
2,0091 gold badge7 silver badges23 bronze badges
edited 8 hours ago
Ivan Di Liberti
asked 8 hours ago
Ivan Di LibertiIvan Di Liberti
2,0091 gold badge7 silver badges23 bronze badges
asked 8 hours ago
Ivan Di LibertiIvan Di Liberti
2,0091 gold badge7 silver badges23 bronze badges
asked 8 hours ago
Ivan Di LibertiIvan Di Liberti
2,0091 gold badge7 silver badges23 bronze badges
2,0091 gold badge7 silver badges23 bronze badges
3
$begingroup$
The original proof by Deligne appeared in SGA4, but it might be a little bit hard to found: it is in the appendix of exposé VI, (which is part II)
$endgroup$
– Simon Henry
8 hours ago
add a comment |
3
$begingroup$
The original proof by Deligne appeared in SGA4, but it might be a little bit hard to found: it is in the appendix of exposé VI, (which is part II)
$endgroup$
– Simon Henry
8 hours ago
3
3
$begingroup$
The original proof by Deligne appeared in SGA4, but it might be a little bit hard to found: it is in the appendix of exposé VI, (which is part II)
$endgroup$
– Simon Henry
8 hours ago
$begingroup$
The original proof by Deligne appeared in SGA4, but it might be a little bit hard to found: it is in the appendix of exposé VI, (which is part II)
$endgroup$
– Simon Henry
8 hours ago
add a comment |
1 Answer
1
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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.
answered 8 hours ago
godeliangodelian
2,7741 gold badge23 silver badges25 bronze badges
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$begingroup$
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.
answered 8 hours ago
godeliangodelian
2,7741 gold badge23 silver badges25 bronze badges
$endgroup$
add a comment |
$begingroup$
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.
answered 8 hours ago
godeliangodelian
2,7741 gold badge23 silver badges25 bronze badges
$endgroup$
add a comment |
$begingroup$
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.
answered 8 hours ago
godeliangodelian
2,7741 gold badge23 silver badges25 bronze badges
$endgroup$
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.
answered 8 hours ago
godeliangodelian
2,7741 gold badge23 silver badges25 bronze badges
edited 8 hours ago
answered 8 hours ago
godeliangodelian
2,7741 gold badge23 silver badges25 bronze badges
answered 8 hours ago
godeliangodelian
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answered 8 hours ago
godeliangodelian
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The original proof by Deligne appeared in SGA4, but it might be a little bit hard to found: it is in the appendix of exposé VI, (which is part II)
$endgroup$
– Simon Henry
8 hours ago