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math.CT2023
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…
math.CT2023
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…
math.CT2023
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…