7 papers · 1 filter
Strongly finitary monads and multi-sorted varieties enriched in cartesian closed concrete categories
Jason Parker
It is a classical result of categorical algebra, due to Lawvere and Linton, that finitary varieties of algebras (in the sense of Birkhoff) are dually equivalent to finitary monads…
Free algebras of topologically enriched multi-sorted equational theories
Jason Parker
Classical multi-sorted equational theories and their free algebras have been fundamental in mathematics and computer science. In this paper, we present a generalization of multi-so…
Enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities
Rory B. B. Lucyshyn-Wright, Jason Parker
Lawvere's algebraic theories, or Lawvere theories, underpin a categorical approach to general algebra, and Lawvere's adjunction between semantics and algebraic structure leads to a…
Presentations and algebraic colimits of enriched monads for a subcategory of arities
Rory B. B. Lucyshyn-Wright, Jason Parker
We develop a general framework for studying signatures, presentations, and algebraic colimits of enriched monads for a subcategory of arities, even when the base of enrichment $\ma…
Inner automorphisms of presheaves of groups
Jason Parker
It has been proven by Schupp and Bergman that the inner automorphisms of groups can be characterized purely categorically as those group automorphisms that can be coherently extend…
Covariant Isotropy of Grothendieck Toposes
Jason Parker
We provide an explicit characterization of the covariant isotropy group of any Grothendieck topos, i.e. the group of (extended) inner automorphisms of any sheaf over a small site.…