Eilenberg - Mac Lane范畴概念在非刚性结构中的推广
An extension of the Eilenberg - Mac Lane concept of category in the case of nonrigid structures
摘要：
非刚性的数学结构可能不再形成通常的艾伦伯格-麦克莱恩范畴，而是更一般的范畴，如伪拓扑所示。在构造包含Schwartz分布的广义函数的微分代数时，使用了伪拓扑的一个相当一般的概念[4- 6，8 -11]。这些代数被证明是方便的解决大类的非线性偏微分方程，见[12，13]和文献引用，以及第46 F 30节在主题分类2000年的美国数学学会，在www.ams.org/index/msc/46Fxx.html的总体，这样的伪拓扑结构不再构成一个通常的艾伦伯格-麦克巷类别，但一个扩展的，这是在这里提出的。其他非刚性的数学结构被提及和简要处理。这是对早期发表的论文[7]的修订和扩充版本。
英文摘要：
Nonrigid mathematical structures may no longer form usual Eilenberg - Mac Lane categories, but more general ones, as illustrated by pseudo-topologies. A rather general concept of pseudo-topology was used in constructing differential algebras of generalized functions containing the Schwartz distributions, [4-6,8-11]. These algebras proved to be convenient in solving large classes of nonlinear partial differential equations, see [12,13] and the literature cited there, as well as section 46F30 in the Subject Classification 2000 of the American Mathematical Society, at www.ams.org/index/msc/46Fxx.html The totality of such pseudo-topologies no longer constitutes a usual Eilenberg - Mac Lane category, but an extended one which is presented here. Other nonrigid mathematical structures are mentioned and treated briefly. This is a revised and augmented version of the earlier published paper [7].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
