Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube Q and the C0-coarse category of their complements. The C0coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants ...

We describe an isomorphism of categories conjectured by Kontsevich. If M and M̃ are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on M and a suitable version of Fukaya’s category of Lagrangian submanifolds on M̃. We prove this equivalence when M is an elliptic curve and M̃ is its dual curve, exhibiting the dictionary in detail. † email: apolish@m...

In this paper we use A∞-modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A∞-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasi-isomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of ...

(In first case we say (F,G2) are an adjoint pair and in the second case we say that (G1, F ) are an adjoint pair.) (2) An object A in a category C is called initial (resp. final) if for every object B in C, HomC(A,B) (resp. HomC(B,A)) is a singleton. Prove that an initial (resp. final) object, if it exists, is unique up to unique isomorphism. Determine if such objects exist in the following cat...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...

The well-known difficulties arising in a classification which is not set-theoretically trivial—involving what is sometimes called a nonsmooth quotient—have been overcome in a striking way in the theory of operator algebras by the use of what might be called a classification functor—the very existence of which is already a surprise. Here the notion of such a functor is developed abstractly, and ...

Notwithstanding known obstructions to this idea, we formulate an attempt to turn quantization into a functorial procedure. We define a category Poisson of Poisson manifolds, whose objects are integrable Poisson manifolds and whose arrows are isomorphism classes of regular Weinstein dual pairs; it follows that identity arrows are symplectic groupoids, and that two objects are isomorphic in Poiss...

Many formulations of proof nets and sequent calculi for Classical Linear Logic (CLL) [7, 8] take it for granted that a type A is identical to its double negation A⊥⊥. On the other hand, since Seely [13], it has been assumed that ∗-autonomous categories [1, 2] are the appropriate semantic models of (the multiplicative fragment of) CLL. However, in general, in a ∗-autonomous category an object A ...

In the following statement, gr denotes the category of free groups of finite rank, VecQ the category of Q-vector spaces, a : gr→ VecQ the composition of abelianisation and rationalisation (a(G) = Gab ⊗ Q) and Λ the j-th exterior power. As usual, Fr is a free group of rank r; gr-Mod is the category of functors from gr to VecQ. Theorem 1. Let F : gr → VecQ be a polynomial functor of degree d and ...