Monads and cocompleteness of categories
Profinite relational structures
Composites of effective descent maps
Descent equivalence
Split extensions and semidirect products of unitary magmas
We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.
Absolutely closed spaces and categories of algebras
Descent for compact 0-dimensional spaces.
On functors which are lax epimorphisms.
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