14 citations · 69 across the 21 of their papers we have counts for
24 papers
Dual adjunctions between enriched algebraic categories
Rory B. B. Lucyshyn-Wright
Working in the setting of enriched algebraic theories for a system of arities, we study several aspects of dual adjunctions between enriched algebraic categories, which we call alg…
V-graded categories and V-W-bigraded categories: Functor categories and bifunctors over non-symmetric bases
Rory B. B. Lucyshyn-Wright
In the well-known settings of category theory enriched in a monoidal category V, the use of V-enriched functor categories and bifunctors demands that V be equipped with a symmetry,…
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…
Centralizer clones relative to a strong limit cardinal
Rory B. B. Lucyshyn-Wright, Darian McLaren
The notion of commutation of operations in universal algebra leads to the concept of centralizer clone and gives rise to a well-known class of problems that we call centralizer pro…
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…
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…