Some Researches Of Poset Category

In this dissertation, we set the finite poset category as our mainly mathematical entities. Using the category language, firstly, we study several important dual notions in finite poset category, such as pushout and pullback, terminal object and initial object, product and coproduct, and so on. Further more, linked together two product—Tensor product and Hadamard product, we give the precise matrices of this two product poset category.Functor is considered as a bridge of the connection between two categories. It is important to understand the relationship of two concrete categories by describing the functor between them. So in chapter five, we put our efforts into studying the functor of two same rank finite poset categories, originally introducing a series of new notions such as chain, matrix functor to present the functor of two same rank finite poset categories in matrix form, besides, a necessary and sufficient condition of a matrix functor considered as a functor between two same rank finite poset categories is given in this chapter.At last, we apply the results of chapter five into finite representation type, point out the possibility of describing the endofunctor of Dynkin diagram D4 in matrix functor pattern, also give one example to show to readers.