Questions tagged [stone-duality]

Given two Heyting algebras $A$ and $B$, let $A+B$ be their coproduct in the category of Heyting algebras. Is it true that the inclusion $A → A+B$ always has a left and a right adjoint ? (Actually, I ...

First let me recall Stone duality in terms of propositional logic. Let $L$ and $K$ be propositional signatures (i.e., sets of propositional variables). Let $T$ be a propositional theory over $L$ and $...

Historically, the theory of ultracategories was invented by Makkai to prove a strong conceptual completeness theorem for first-order logic, roughly: if $T$ and $S$ are two first-order theories such ...

When is the opposite of the category of algebras of a Lawvere theory an extensive category? Any necessary or sufficient conditions on the Lawvere theory will be interesting to me. Here's why I'm ...