From the 1 of 4 linked papers with an AI index.
4 papers
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…
Algebraic coherators, controlled theories, and Grothendieck realizations
Johnathon Taylor
The paper introduces a direct construction of algebraic coherators for Grothendieck ∞‑groupoids via the algebraic small object argument, defines unreduced and reduced Grothendieck…
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…
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…