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...

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...

A notion of central importance in categorical topology is that of topological functor. A faithful functor E → B is called topological if it admits cartesian liftings of all (possibly large) families of arrows; the basic example is the forgetful functor Top→ Set. A topological functor E → 1 is the same thing as a (large) complete preorder, and the general topological functor E → B is intuitively...

In this paper we develop the theory of topological categories over a base category, that is, a theory of topological functors. Our notion of topo-logical functor is similar to (but not the same) the existing notions in the literature (see [2] 7.3), and it aims at the same examples. In our sense, a (pre) topological functor is a functor that creates cartesian families. A topological functor is, ...