Related papers: Calculations for Plus Constructions
This Bachelor's thesis studies Adelman's construction of the universal abelian category of an additive category. It furthermore extends the construction such that it also applies to transformations between additive functors.
A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable…
In this paper we show that the Day monoidal product generalises in a straightforward way to other algebraic constructions and partial algebraic constructions on categories. This generalisation was motivated by its applications in logic, for…
We develop the theory of (op)fibrations of 2-multicategories and use it to define abstract six-functor-formalisms. We also give axioms for Wirthm\"uller and Grothendieck formalisms (where either $f^!=f^*$ or $f_!=f_*$) or intermediate…
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…
We construct the quantum s-tuple subfactors for an AFD II_1 subfactor with finite index and depth, for an arbitrary natural number s. This is a generalization of the quantum multiple subfactors by J.Erlijman and H.Wenzl, which generalizes…
Additive categories play a fundamental role in mathematics and related disciplines. Given an additive category equipped with a biadditive functor, one can construct its category of extensions, which encodes important structural information.…
The problem of determining gauge and monoidal equivalence classes of fusion categories is considered from the perspective of geometric invariant theory. It is shown that the gauge (or monoidal) class of a fusion category is determined by…
We present a new method, the Subdivision Construction, for proving the finite model property (the fmp) for broad classes of modal logics and modal rule systems. The construction builds on the framework of stable canonical rules, and…
In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mostly symmetric ones, for which we propose a physical interpretation. These are…
In this paper we propose unifying the categories of cochain complexes $\text{Ch}(\mathcal{C})$ and modules $\widehat{A}\text{-mod}$ over a repetitive algebra $\widehat{A}$. Motivated by their striking similarities and importance, we…
We define and study opfibrations of $V$-enriched categories when $V$ is an extensive monoidal category whose unit is terminal and connected. This includes sets, simplicial sets, categories, or any locally cartesian closed category with…
In this survey paper we give account of several approaches to the strictification and non-strictification of monoidal categories, which are constructions that turn a monoidal category into a (non-)strict one monoidally equivalent to the…
We define a class of monoidal categories whose morphisms are diagrams, and which are enhancements and generalisations of the Brauer category obtained by adjoining infinitesimal braids, "coupons" and poles. Properties of these categories are…
There is an ``algebraisation'' of the notion of weak factorisation system (w.f.s.) known as a natural weak factorisation system. In it, the two classes of maps of a w.f.s. are replaced by two categories of maps-with-structure, where the…
Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full…
We provide details of the proof of Lurie's theorem on operadic Kan extensions. Along the way, we generalize the construction of monoidal envelopes of $\infty$-operads to families of $\infty$-operads and use it to construct the fiberwise…
We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation,…
We continue the study of enriched infinity categories, using a definition equivalent to that of Gepner and Haugseng. In our approach enriched infinity categories are associative monoids in an especially designed monoidal category of…
We prove that an enriched $\infty$-category is completely determined by its enriched presheaf category together with a `marking' by the representable presheaves. More precisely, for any presentably monoidal $\infty$-category $\mathcal{V}$…