Related papers: Data types with symmetries and polynomial functors…
Polynomial functors are a categorical generalization of the usual notion of polynomial, which has found many applications in higher categories and type theory: those are generated by polynomials consisting a set of monomials built from sets…
This note extends Quillen's Theorem A to a large class of categories internal to topological spaces. This allows us to show that under a mild condition a fully faithful and essentially surjective functor between such topological categories…
Awodey, later with Newstead, showed how polynomial functors with extra structure (termed ``natural models'') hold within them the categorical semantics for dependent type theory. Their work presented these ideas clearly but ultimately led…
Motivated by potential applications to theoretical computer science, in particular those areas where the Curry-Howard correspondence plays an important role, as well as by the ongoing search in pure mathematics for feasible approaches to…
Recently, there has been renewed interest in the theory and applications of de Paiva's dialectica categories and their relationship to the category of polynomial functors. Both fall under the theory of generalized polynomial categories,…
We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…
We show that the free construction from multicategories to permutative categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induced functor between categories of algebras is an equivalence…
We give a specific cylinder functor for semifree dg categories. This allows us to construct a homotopy colimit functor explicitly. These two functors are "computable", specifically, the constructed cylinder functor sends a dg category of…
We prove that commutative semirings in a cartesian closed presentable $\infty$-category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product-preserving functors from the $(2,1)$-category of bispans of finite sets. In other…
We study polynomial comonads and polynomial bicomodules. Polynomial comonads amount to categories. Polynomial bicomodules between categories amount to parametric right adjoint functors between corresponding copresheaf categories. These may…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a…
Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the…
The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the…
We upgrade the classical operation of \textit{isomonodromic deformations} along a path $\gamma$ to a functor $\mathbb{P}_{\gamma}$ between categories of flat connections with logarithmic singularities along a divisor $D$, which itself…
This dissertation comprises three collections of results, all united by a common theme. The theme is the study of categories via algebraic techniques, considering categories themselves as algebraic objects. This algebraic approach to…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
An objective of the theory of combinatorial groupoids is to introduce concepts like "holonomy", "parallel transport", "bundles", "combinatorial curvature" etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes,…
The theory developed by Gambino and Kock, of polynomials over a locally cartesian closed category E, is generalised for E just having pullbacks. The 2-categorical analogue of the theory of polynomials and polynomial functors is given, and…
The question "What is category theory" is approached by focusing on universal mapping properties and adjoint functors. Category theory organizes mathematics using morphisms that transmit structure and determination. Structures of…