Some Researches About Pullback Functors

Functor is a key concept in category theory and also the basic means of study-ing relations between categories. While, pullback is another important concept, which has an important role in homological algebra, representation theory of algebra, rings and modules theory, and so on. This thesis regards pullback as an functor and considers pullback-functors’properties on Cocomma categories. The introduction recommends the background and current status, and also summarizes the main results and gives some notations presented in the thesis. The thesis is divided into four chapters.The first chapter considers T-pullback-invariant morphisms and (T,.F)-pullback-invariant morphisms in Abelian categories. Meanwhile, it proves that the (T,F)-pullback-invariant morphism class (T, F)e is preserved by reverse limits when the morphism class T is.The second chapter combines pullback with the functor. After an introduc-tion of the pullback-functor Fc:l/C×l/C→l/C into Cocomma categories, it discusses some related properties. Finally, an example is given to explain the application of pullback-functors on road algebra.In chapter three, for an given object Mm∈l/C, it considers whether the pullback-functor Fc(Mm,-) preserves morphism’s properties and limit of Cocomma categories or not, including essential monomorphism, one-side almost split morphism and irreducible morphism.The fourth chapter sums up the main results of this thesis.