1 citations · 1 across the 4 of their papers we have counts for
5 papers
Idempotence for relative monads
Nathanael Arkor, Andrew Slattery
We study the concept of idempotence for relative monads, which exhibits several subtleties not present for non-relative monads. In particular, there is a bifurcation of notions of…
Magmal characterisations of cocartesian categories
Nathanael Arkor
We present a survey of characterisations of cocartesian categories in terms of monoidal categories - and, more generally, magmal categories - satisfying additional properties. In p…
Bicategories of algebras for relative pseudomonads
Nathanael Arkor, Philip Saville, Andrew Slattery
We introduce pseudoalgebras for relative pseudomonads and develop their theory. For each relative pseudomonad , we construct a free--forgetful relative pseudoadjunction that exh…
Enhanced 2-categorical structures, two-dimensional limit sketches and the symmetry of internalisation
Nathanael Arkor, John Bourke, Joanna Ko
Many structures of interest in two-dimensional category theory have aspects that are inherently strict. This strictness is not a limitation, but rather plays a fundamental role in…
Algebraic models of simple type theories: a polynomial approach
Nathanael Arkor, Marcelo Fiore
We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of s…