The Property And Popularize Of The Pullback Diagram In The Category Of Semimodules

In this dissertation we introduce the concepts of the pullback、n-pullback andpushout and the properties of it in the category of semimodules.The thesis falls intothree parts.In the first section, we introduce the concept of the pullback,prove the existenceand the uniqueness of the pullback,then discuss the retained properties betweenpullback and semimodule family A_i （i=1,2）in the condition ofP={（a₁, a₂）∈A₁×A₂|f₁（a₁）=f₂（a2）}.In the second section,we introduce the concept of the pullback,prove theexistence and the uniqueness of then-pullback;then discuss the retained propertiesbetweenn-pullback and semimodule family in the condition ofP={（a₁,a₂,...,a_n）∈A₁×A₂×...×An|fi（a_i）=fj（a j）,i≠j，i,j=1,2,......n}.In the last, we introduce the concept and properties of the pushout andn-pushout, so get some good conclusions.