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...

Let T be a 1-sorted structure. The functor TotFamT yielding a family of subsets of T is defined by: (Def. 1) TotFamT = 2 carrier of T . The following proposition is true (1) For every set T and for every family F of subsets of T holds F is countable iff F c is countable. Let us note that Q is countable. The scheme FraenCoun11 concerns a unary predicate P, and states that: {{n};n ranges over ele...

Let us assume we are given a totally contra-multiplicative functor τ̃ . It has long been known that |T | = 1 [17, 13, 19]. We show that every countably p-adic polytope is almost surely canonical and Euclidean. Moreover, here, positivity is obviously a concern. In [14], the main result was the description of hyper-trivial, characteristic, Cantor domains.

In a previous paper, we investigated the relation between the initial algebra and terminal coalgebra for an endofunctor on the category of sets. In this one we study conditions on a functor to be algebraically compact, which means that the canonical comparison morphism between those objects is an isomorphism. Introduction Suppose C is a category and T : C −→ C is a functor. In both [Barr, 1991]...

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...

We present a general framework for logics of transition systems based on Stone duality. Transition systems are modelled as coalgebras for a functor T on a category X . The propositional logic used to reason about state spaces from X is modelled by the Stone dual A of X (e.g. if X is Stone spaces then A is Boolean algebras and the propositional logic is the classical one). In order to obtain a m...