An Inverse Limit Of The Structure, Monoidal Category

The main results of this paper as follows. Firstly,we present the definition of Cowedge product in monoidal category.Secondly, construct an inverse limit related to the definition, and prove the compatibility between algebra system and the inverse limit.Finally, we give a proof of an epimorphism theorem for monoidal category on this basis.This thesis can be separated into 4 chapters.Chapter 1 introduces in this paper the development of research topics related to the context of this paper, and some symbols.Chapter 2 is mainly some basic concepts and theories, and based on this, gives the definition of Cowedge product .In chapter 3 we study the properties of Cowedge product specifically.Inspired by [21], by use of the form of Duality,we get some Propositions ,lemmas and theorems related to them.We make the n-th Cowedge product and present the inverse limit related to the n-th Cowedge product.Chapter 4 is the main proof of an epimorphism theorem corresponding to the inverse limit.The theorem as follows:Let (M, (?), 1) be a complete and abelian Monoidal category, whose tensor product functor keep the left exact sequence. A,D are algebras in (M.Letδ:Aâ†'D,f:Câ†'A be homomorphism of algebra in M,and satisfy the following three conditions:(1)δis an algebra epimorphism so thatδin notation3.2.4 is an algebra epimorphism.(2) The inverse limit is an exact functor.(3) f : Câ†'Ais an homomorphism of algebra andδ₂ o f : Câ†'D∨_A D is an epimorphism .Thenδo f : Câ†'D_A is an epimorphism.