Another Approach to Topological Descent Theory

In the category T op of topological spaces and continuous functions, we prove that surjective maps which are descent morphisms with respect to the class E of continuous bijections are exactly the descent morphisms, providing a new characterization of the latter in terms of subfibrations E(X) of the basic fibration given by T op/X which are, essentially, complete lattices. Also effective descent morphisms are characterized in terms of effective morphisms with respect to continuous bijections. For classes E satisfying suitable conditions, we show that the class of effective descent morphisms coincides with the one of effective E-descent morphisms.     

The Drazin Inverse of a Morphism with a Sequence of (epic, monic) Factorizations

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｉｎ [1 ],ｔｈｅａｕｔｈｏｒｄｅｆｉｎｅｄａｃｃｕｒａｔｅｌｙｔｈｅＤｒａｚｉｎｉｎｖｅｒｓｅｏｆａｍｏｒｐｈｉｓｍ .Ｐｒｅｖｉｏｕｓｌｙ ,ｓｏｍｅｎｅｃｅｓｓａｒｙａｎｄｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓｗｅｒｅｏｂｔａｉｎｅｄｆｏｒａｍｏｒｐｈｉｓｍｗｉｔｈ (ｅｐｉｃ ,ｍｏｎｉｃ)ｆａｃｔｏｒｉｚａｔｉｏｎｔｏｈａｖｅｔｈｅｇｒｏｕｐｉｎｖｅｒｓｅ (ｓｅｅ [2 ],Ｔｈｅｏｒｅｍ 1 )ａｎｄｔｈｅＤｒａｚｉｎｉｎｖｅｒｓｅｏｆａｍａｔｒｉｘｏｖｅｒｔｈｅｃｏｍｐ…     

Free Adjunction of Morphisms

We develop a general setting for the treatment of extensions of categories by means of freely adjoined morphisms. To this end, we study what we call composition graphs, i.e. large graphs with a partial binary operation on which we impose only rudimentary requirements. The quasicategory thus obtained contains the quasicategory of all categories as a full reflective subquasicategory; we characterize composition graphs for which this reflexion is of a particularly simple nature.This leads to the concept of semicategory; we apply semicategories to solve characterization problems concerning absolutely initial sources, absolute monosources and potential sections. For instance, we show that in any category, the absolutely initial sources are precisely the sources that contain a section.     

R~N中一类(p,q)-Laplacian椭圆方程组的多重正解

研究了一类(p,q)-Laplacian拟线性椭圆方程组问题,利用Nehari流形和LjusternikSchnirelmann畴数理论,探讨了位势函数f(x)如何影响这类方程组正解的个数.     

Twisted Orlicz algebras,II

Let G be a locally compact group, let be a 2‐cocycle, and let () be a complementary pair of strictly increasing continuous Young functions. We continue our investigation in [14] of the algebraic properties of the Orlicz space with respect to the twisted convolution ? coming from Ω. We show that the twisted Orlicz algebra posses a bounded approximate identity if and only if it is unital if and only if G is discrete. On the other hand, under suitable condition on Ω, becomes an Arens regular, dual Banach algebra. We also look into certain cohomological properties of , namely amenability and Connes‐amenability, and show that they rarely happen. We apply our methods to compactly generated group of polynomial growth and demonstrate that our results could be applied to variety of cases.