Gegenstand der vorliegenden Arbeit sind Dualitäten in Trikategorien. Diese Arbeit
entwickelt einen Begriff von Dualitäten in allgemeinen Trikategorien, der motiviert ist von …

Linear bicategories are a generalization of ordinary bicategories in which there are two
horizontal (1-cell) compositions corresponding to the “tensor” and “par” of linear logic …

We introduce a weakening of the notion of fusion 2-category given in arXiv: 1812.11933.
Then, we establish a number of properties of (multi) fusion 2-categories. Finally, we describe …

In this paper we answer the question:what kind of a structure can a general multicategory be
enriched in?'The answer is, in a sense to be made precise, that a multicategory of one type …

We define the phrase 'category enriched in an fc-multicategory'and explore some examples.
An fc-multicategory is a very general kind of two-dimensional structure, special cases of …

We show how the notion of intercategory encompasses a wide variety of three-dimensional
structures from the literature, notably duoidal categories, monoidal double categories …

We prove that the Drinfeld center of a fusion 2-category is invariant under Morita
equivalence. We go on to show that the concept of Morita equivalence between connected …

Bangor University DOCTOR OF PHILOSOPHY Aspects of multiple categories Al-Agl, Fahd Ali
A. Page 1 Bangor University DOCTOR OF PHILOSOPHY Aspects of multiple categories Al-Agl …

In this thesis, we introduce Cartesian double categories, motivated by the work of Carboni,
Kelly, Walters, and Wood on Cartesian bicategories. Moving from bicategories to the slightly …

We establish tetrahedral symmetries of 6j-symbols for arbitrary fusion categories under
minimal assumptions. As a convenient tool for our calculations we introduce the notion of a …