Amenable category is a variant of the Lusternik-Schnirelman category, based on covers by amenable open subsets. We study monotonicity problem for degree-one maps and relation between topological complexity.

In this work, we describe an adjunction between the comma category of Set-based monads under the V -powerset monad and the category of associative lax extensions of Set-based monads to the category of V -relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.

Galois connection in category theory play an important role inestablish the relationships between different spatial structures. Inthis paper, we prove that there exist many interesting Galoisconnections between the category of Alexandroff $L$-fuzzytopological spaces, the category of reflexive $L$-fuzzyapproximation spaces and the category of Alexandroff $L$-fuzzyinterior (closure) spaces. This ...

The concept of indexing of a category (a part of indexed category, see [14]) is introduced as a pair formed by a many sorted category and a many sorted functor. The indexing of a category C against to [14] is not a functor but it can be treated as a functor from C into some categorial category (see [1]). The goal of the article is to work out the notation necessary to define institutions (see [...

The funding proposed here will provide an apparatus for precisely displaying 3D sounds, advancing understanding of how humans use sound to locate sources and analyze their environment, and exploring how audition affects and is affected by vision. Specifically the proposed research aims to answer the complementary questions • What information is used to locate the source of a sound within a list...