Coherent topos

In mathematics, a coherent topos is a topos generated by a collection of quasi-compact quasi-separated objects closed under finite products. ^[1]

Deligne's completeness theorem says a coherent topos has enough points. ^{[2] [3] [4]}

See also

• Spectral space
• Pyknotic set

References

1. Jacob Lurie, Categorical Logic (278x). Lecture 11. Definition 6.
2. Frot, Benjamin (2013). "Godel's Completeness Theorem and Deligne's Theorem". arXiv: 1309.0389 [math.LO].
3. "Deligne completeness theorem in nLab".
4. Grothendieck, A. (1972). "Site et Topos etales d'un schema, 9. Appendice. Critère d'existence de points par P. Deligne". Théorie des Topos et Cohomologie Etale des Schémas. Lecture Notes in Mathematics. Vol. 270. pp. 341–365. doi:10.1007/BFb0061323. ISBN   978-3-540-06012-3.

• Peter Johnstone, Sketches of an Elephant
• Reyes, Gonzalo E. (1977). "Sheaves and concepts : A model-theoretic interpretation of Grothendieck topoi". Cahiers de Topologie et Géométrie Différentielle Catégoriques. 18 (2): 105–137.
• "Continuously Variable Sets; Algebraic Geometry = Geometric Logic" (PDF). Studies in Logic and the Foundations of Mathematics. 80: 135–156. 1975. doi:10.1016/S0049-237X(08)71947-5. ISBN   978-0-444-10642-1 – via The F. William "Bill" Lawvere Archives.

External links

• "coherent topos in nLab". ncatlab.org.