Let L be an arbitrary orthomodular lattice. There is a one to one correspondence between orthomodular sublattices of L satisfying an extra condition and quantic quantifiers. The category of orthomodular lattices is equivalent to the category of posets having two families of endofunctors satisfying six conditions.

We investigate vertex operator algebras L(k, 0) associated with modular-invariant representations for an affine Lie algebra A (1) 1 , where k is ’admissible’ rational number. We show that VOA L(k, 0) is rational in the category O and find all irreducible representations in the category of weight modules.

A. Introduction: There are several useful reviews on rare kaon decays and related topics [1–14]. Activity in rare kaon decays can be divided roughly into four categories: 1. Searches for explicit violations of the Standard Model 2. Measurements of Standard Model parameters 3. Searches for CP violation 4. Studies of strong interactions at low energy. The paradigm of Category 1 is the lepton flav...

We present a comparative study of certain invariants defined for group actions and their analogues orbifolds. In particular, we prove that Fadell's equivariant category $G$-spaces coincides with the Lusternik-Schnirelmann orbifolds when is finite.

In this paper, for a complete residuated lattice L, we present the categorical properties of ?-neighborhood spaces and their relationships to neighborhood stratified L-neighborhood spaces. The main results are: (1) category is topological category; (2) can be embedded in as reflective subcategory, when L meet-continuous lattice, subcategory; (3) continuous (resp., spaces) simultaneously corefle...

Let f : G → A be a surjective homomorphism of transitive groupoid schemes and let L denote the kernel of f . The exact sequence of groupoid schemes 1 → L → G → A → 1 induces a sequence of functors between the categories of finite representations of these groupoid schemes Repf (A) → Repf (G) → Repf (L). We show that the category Repf (L) is a quotient category of Repf (G) by Repf (A) in an appro...

The results presented here first appeared in Chapter 2 of [Mrn1] and were announced with proofs in [MM1]. Our motivation came from [KMS], that introduces the class of direct limits of finite abstract order spaces, a theory due to M. Marshall ([Mar1]). The theory of special groups, introduced in [DM2], is a first-order axiomatization of the algebraic theory of quadratic forms, and there is a nat...

We study FTOP (L), a fuzzy category related to topology with fuzzy functions in the role of morphisms.