Coherent topos explained

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] William Lawvere noticed that Deligne's theorem is a variant of the Gödel completeness theorem for first-order logic.^[3]

See also

• Spectral space
• Pyknotic set

References

• Peter Johnstone, Sketches of an Elephant

External links

• https://ncatlab.org/nlab/show/coherent+topos

Notes and References

1. Jacob Lurie, Categorical Logic (278x). Lecture 11. Definition 6.
2. B. Frot, Gödel’s Completeness Theorem and Deligne’s Theorem, arXiv:1309.0389 (2013).
3. https://ncatlab.org/nlab/show/Deligne+completeness+theorem