Research On The Category Of Internal Group And Its Properties

In the 1960 s,Ehresmann proposed the theory of internal categroy for the first time,which was the important content of the study of category theory.Lawvere put forward the categorical algebra theory and functor model theory in order to introduced the concept of internal group objects in his doctoral thesis,It further reveals the intrinsic and essential properties of things.In this paper,based on the idea of Lawvere,we researched the product,equalizer,pullback and other limit theory in the category of internal group.This paper was divided into three chapters as follow:The first chapter: This paper introduced some basic concepts and theorems in the category,and gives the complete proof of the main lemmas.The second chapter: Based on the method of Lawvere categorical algebra theory and functor model theory.We introduced the concept of internal group objects and the category of internal group.Then we giave the model of internal group objects in specific category.The third chapter: We mainly discussed the closeness of products and properties of monomorphism,equalizer,and pullback in the category of internal group.Lastly,we gave the relationship between these concepts of the internal group categroy and the corresponding concepts of the base category.