Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made can have noticeable effects on what categorical constructions are permissible. In this expository paper we summarize and compare a number of such “set-theore...

We construct a functor from the derived category of homotopy Gerstenhaber algebras, g, with finite-dimensional cohomology to the purely geometric category of so-called F ∞-manifolds. The latter contains Frobenius manifolds as a subcategory (so that a pointed Frobenius manifold is itself a homotopy Gerstenhaber algebra). If g happens to be formal as a L ∞-algebra, then its F ∞-manifold comes equ...

Energy efficiency is a major concern in Wireless Sensor Networks (WSNs). Many clustering algorithms have been proposed for such a purpose. This paper investigates the existing clustering algorithms. The algorithms have been classified and some representatives are described in each category. After analyzing the strengths and the weaknesses of each category, an important characteristic of WSNs is...

We construct a functor from the derived category of homotopy Gerstenhaber algebras, g, with finite-dimensional cohomology to the purely geometric category of so-called F ∞-manifolds. The latter contains Frobenius manifolds as a subcategory (so that a pointed Frobenius manifold is itself a homotopy Gerstenhaber algebra). If g happens to be formal as a L ∞-algebra, then its F ∞-manifold comes equ...

We propose a simplified definition of Quillen’s fibration sequences in pointed model category that fully captures the theory, although it is completely independent concept action. This advantage arises from understanding homotopy