The goal of this paper is to provide the last equivalence needed in order identify all known models for ( ∞ , 2 ) $(\infty,2)$ -categories. We do by showing that Verity's model saturated 2-trivial complicial sets equivalent Lurie's $\infty$ -bicategories, which, turn, has been shown be other A key technical input given identifying notion -bicategories with weak a step which allows us understand...

Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-dimensional topology. We study a generalization of this notion, namely rigid algebras in an arbitrary 2-category. Examples include G-graded fusion 1-categories, G-crossed 1-categories. explore the properties 2-categories modules bimodules over algebra, by giving criterion for existence right left adjoints. Then, we co...

The main goal of this paper is to classify ?-module categories for the SO(3)2m modular tensor category. This done by classifying nimrep graphs and cell systems, in process we also SO(3) invariants. There are module type A, E their conjugates, but there no orbifold (or D) categories. We present a construction subfactor with principal graph given fusion rules fundamental generator introduce Frobe...

We show that relations in Homflypt type skein theory of an oriented [Formula: see text]-manifold text] are induced from a text]-groupoid defined the fundamental space singular links text]. The module by homomorphisms related to string topology. They appear representation groupoid into free modules on set model objects. construction is singularity stratification and relates Vassiliev theory. Sev...