# nLab Makkai duality

category theory

duality

## Idea

Makkai duality is a kind of syntax-semantics duality, due to Michael Makkai, relating pretoposes (categories having to do with the syntax of first-order logic) and ultracategories (which are a way of capturing the semantics of first-order logic). This leads to a proof of conceptual completeness for first-order logic.

## References

Some more general variants are achieved in

• Marek W. Zawadowski, Descent and duality, Annals of Pure and Applied Logic 71, n.2 (1995), 131–188

• Henrik Forssell, First-order logical duality, Ph.D. thesis, Carnegie Mellon U. 2008, pdf

Last revised on April 24, 2020 at 06:28:57. See the history of this page for a list of all contributions to it.