1 citations · 1 across the 12 of their papers we have counts for
14 papers
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…
Star Anagram Detection and Classification
Jason Parker, Dan Barker
A star anagram is a rearrangement of the letters of one word to produce another word where no letter retains its original neighbors. These maximally shuffled anagrams are rare, com…
Exponentiability in categories of relational structures
Jason Parker
For a relational Horn theory , we provide useful sufficient conditions for the exponentiability of objects and morphisms in the category $\mathbb{T}\text{-}\mathsf{Mod}…
Diagrammatic presentations of enriched monads and varieties for a subcategory of arities
Rory B. B. Lucyshyn-Wright, Jason Parker
The theory of presentations of enriched monads was developed by Kelly, Power, and Lack, following classic work of Lawvere, and has been generalized to apply to subcategories of ari…
Extensivity of categories of relational structures
Jason Parker
We prove that the category of models of any relational Horn theory satisfying a mild syntactic condition is infinitely extensive. Central examples of such categories include the ca…
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…
Locally bounded enriched categories
Rory B. B. Lucyshyn-Wright, Jason Parker
We define and study the notion of a locally bounded enriched category over a (locally bounded) symmetric monoidal closed category, generalizing the locally bounded ordinary categor…
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.…
Polymorphic Automorphisms and the Picard Group
Pieter Hofstra, Jason Parker, Philip J. Scott
We investigate the concept of definable, or inner, automorphism in the logical setting of partial Horn theories. The central technical result extends a syntactical characterization…
Isotropy Groups of Free Racks and Quandles
Jason Parker
In this article, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, we show that the usual inner automorphisms of suc…
Isotropy and Combination Problems
Jason Parker
In a previous paper, the author and his collaborators studied the phenomenon of isotropy in the context of single-sorted equational theories, and showed that the isotropy group of…