6 papers
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.…
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…