左R-n模的范畴与Hom函子

正合列问题是同调代数的基本问题之一。在Abel范畴的同调代数中,先有核的概念再讨论正合列的概念。但,因n-予加法范畴不具有零对象,欲讨论正合列,对其引进拟核。本文对左R-n模的范畴_R~M_n~l讨论了与拟核相应的正合列;把Hom函子推广到_R~M_n~l上,讨论了它关于拟正合列、弱双积、正向系统的正向极限的不变性。至于对带终对象的范畴的正合列的讨论我们将在中进行。     

关于微分同胚的一个充分必要条件

确定两个流形是否C^r-微分同胚是微分流形研究中的重要课题,本文定义了反层的概念,给出了反层范畴,由此找到两个微分流形,C^r-微分同胚的特征刻画,于是给出了一种较以往更优的判定法．     

TOPOLOGIES GENERATED BY FUNCTORS

1. This note aims to introduce the notion of the categories with topologies and to discuss topologies generated by functors. A topological semigroup is a category with topologies, in addition, Propositions 10 and 11 will show the generated topologies compatible with adjoint equivalences and bijective half-functors (which are generalized inverse operations in an n-preadditive category, see [1]). Thus, we can believe that there are natural connections between topological and algebraic structures in category structure. In this direction, we shall propose several papers and this note will be an introduction of them.     

在具有终对象的范畴内的正合列

本文对于具有终对象的范畴定义了四个一般正合列．在Ａｂｅｌ范畴同调代数里，对于具有零对象的任何范畴四个一般正合列与通常的正合列相同     

范畴C-cr的一些性质

O. In [1], we have shown the cusp catastrophy is the general mathematical model of the treatment based on syndrome differentiation, but the following phenomenons often happen: An old man may die without any local pathological change; A yong man can live well with some serious local pathological changes. In mechanics, there are many similar facts. Then, confronts us a new problem:     

Hom Functors from A Regular Category

This paper aims to show the exactness of Hom functors with domain a regular category and codomain the category set. I°In [Ⅰ], we put forward a problem: To what degree and to which categories with ferminal objects can HAA (homological algebra in abelian categories)be naturally extended? By "naturally"we mean that the generalized theory degenerate into the theory of HAA when the terminal objects are nullS.     

n-予加法范畴中的弱上积与极限

在Abel范畴的同调代数中,双积和环模的正向系统的正向极限都是重要的基本概念。在那里,由于Abel范畴具有零对象这些概念的讨论就比较简单。本文给出这些概念在n-予加法范畴中的一种推广,我们的困难在于n-予加法范畴只具有终对象。本文的结果表明在n-予加法范畴中这些概念的讨论可以不使用零对象,另一方面也给出在Abel范畴场合中讨论极限时使用零对象的实质的一个解剖。