Some Researches On The Limit Of Categories And The Limit Categories And Its Applications

Categories and the properties of extensions of the categories are important branches of the math research, arouse the cross-development among many subjects and yield a series of profound and the challenging research results. In this thesis,we research on the limits of the categories and limit-category,specific characterization of the limits, and systematically study the prevervability of some properties on the limit categories,and discussese the relations with two extensions (Trivial extensions and Recollement) of the category and get many interesting results.The first chapter introduces the background and the recent development,give an outline of main results of this dissertation.The second chapter characterises the direct limit of direct system of pre-order(poset) of the quiver basis on quiver, specially characterises the direct limit of direct system of pre-order(poset) of two special quivers(Dynkin and Euclidean).The third chapter introduces category of representations and limit-categories of the quiver,and dicuss relations between limit-categories and category of represen-tations,get the limit-categories of equivalent to categories of modules.The fourth chapter studies the right extension of the right-complete abelian cat-egories,and show that the limit category of the right extension of the right-complete abelian categories is isomorphic to the right extension of the limit category of the right-complete abelian category.The fifth chapter uses the recollements of abelian categories to construct a recollement of their respective limit categories.