8 papers
A Tale of Two Paths
Johnathon Taylor
We provide a new presentation for a cylinder object inside of the category of co-globular -groupoids. We prove that the cylinder construction that Lanari provides is isomor…
Tensor products, internal homs, and model structures in two dimensional category theory
Johnathon Taylor
In this paper, we introduce a new symmetric monoidal structure on , called the \emph{graph tensor product}, with unit given by the terminal category. This tensor prod…
Controlled theories, categorification, and homotopification
Johnathon Taylor
In this paper, we introduce the notion of a controlled theory, originally developed in the author's thesis, as a structural tool for the study of higher categorical algebra. We def…
Algebraic coherators, controlled theories, and Grothendieck realizations
Johnathon Taylor
We introduce a construction of algebraic coherators for Grothendieck -groupoids using the algebraic small object argument, replacing previous approaches we have used based…
An Inductive Strategy Towards a Solution to the Generalized Homotopy Hypothesis
Johnathon Taylor
Using the theory of distributive series of monads, we construct an -coherator called the \emph{inductive coherator}. The category of models out of the inductive coherat…
Chaos in Topological Spaces
John Taylor
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space…