In this work, using the functoriality of Drinfeld center fusion categories, we generalize full simple separable algebras in a fixed category to all categories. This generalization produces new functor, which involves both and is called pointed functor. We prove that functor symmetric monoidal equivalence. It turns out provides precise rather complete mathematical formulation boundary-bulk relat...

We introduce and discuss the notion of naturally full func-tor. The definition is similar to the definition of separable functor: a naturally full functor is a functorial version of a full functor, while a separable functor is a functorial version of a faithful functor. We study general properties of naturally full functors. We also discuss when func-tors between module categories and between c...

Maschke functors, semisimple functors and separable functors of the second kind. Abstract We introduce separable functors of the second kind (or H-separable functors) and H-Maschke functors. H-separable functors are generalizations of separable functors. Various necessary and sufficient conditions for a functor to be H-separable or H-Maschke, in terms of generalized (co)Casimir elements (integr...

Abstract Let Q denote the cyclic group of order two. Using Tate diagram we compute RO ( )-graded coefficients Eilenberg–MacLane -spectra and describe their structure as modules over spectrum Burnside Mackey functor. If underlying functor is a Green functor, also obtain multiplicative on coefficients.

We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with natural functor from the Fukaya category matrix factorizations constructed model. As applications, it is applied elliptic orbifolds, punctured Riemann surfaces and certain non-compact Calabi-Yau threefolds construct their mirror...