We study algebraic properties of the Brandt λ-extensions of monoids with zero and non-trivial homomorphisms between the Brandt λ-extensions of monoids with zero. We introduce finite, compact topological Brandt λextensions of topological semigroups and countably compact topological Brandt λ-extensions of topological inverse semigroups in the class of topological inverse semigroups and establish ...

This paper concerns open, closed, and open-closed topological conformal field theories. We show that the category of open topological conformal field theories, at all genera, is homotopy equivalent to a category of Calabi-Yau A∞ categories. For each such, we show that there is a universal closed TCFT, which is the initial element in the category of compatible open-closed TCFTs. The homology of ...

For a symmetric monoidal-closed category V and a suitable monad T on the category of sets, we introduce the notion of reflexive and transitive (T,V)-algebra and show that various old and new structures are instances of such algebras. Lawvere’s presentation of a metric space as a V-category is included in our setting, via the Betti-Carboni-Street-Walters interpretation of a V-category as a monad...

The definition of a category of (T,V)-algebras, where V is a unital commutative quantale and T is a Set-monad, requires the existence of a certain lax extension of T. In this article, we present a general construction of such an extension. This leads to the formation of two categories of (T,V)-algebras: the category Alg(T,V) of canonical (T,V)-algebras, and the category Alg(T′,V) of op-canonica...

Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CW-complex. We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such th...

Carbon nanoscrolls (CNSs) belong to the same class of carbon-based nanomaterialsas carbon nanotubes. As a new category of quasi one dimensional material Graphene Nanoscroll (GNS) has captivated the researchers recently because of its exceptional electronic properties like having large carrier mobility. GNS shape has open edges and no caps unlike Single Wall Nanotubes (SWNTs) which are wou...

In this paper we have characterized the epimorphisms in the full subcategory of Hausdorff fuzzy topological spaces (introduced by Srivastava et al.[10]) of the category FTS of fuzzy topological spaces and fuzzy continuous functions using the Salbanytype closure operator.

We carefully define and study C∗-algebras over topological spaces, possibly non-Hausdorff, and review some relevant results from point-set topology along the way. We explain the triangulated category structure on the bivariant Kasparov theory over a topological space and study the analogue of the bootstrap class for C∗-algebras over a finite topological space.

At the heart of the axiomatic formulation of 1+1-dimensional topological field theory is the set of all surfaces with boundary assembled into a category. This category of surfaces has compact 1-manifolds as objects and smooth oriented cobordisms as morphisms. Taking disjoint unions gives a monoidal structure and a 1+1-dimensional topological field theory can be defined to be a monoidal functor ...

Given a concrete category (A, U) over X, the paper presents a fuzzification scheme of algebraic and topological structures over the category X(A) of A-valued X-objects with a fixed basis A.