The Properties Of The Pushouts Category

In this thesis, we mainly study the pushouts category C~â—‡ in which the pushouts are the objects and the pushouts morphisms are the morphisms. In the category C~â—‡, we get some results of the coknernel, coproduct and additive category.First and foremost of all, some fundamental concepts are introduced. Then the pushouts morphisms, the induced morphisms and the composite of pushouts morphisms are well defined.What's more, we prove two propositions that connect with the context.Last but not the least, according to the pushouts category , we obtain the theory of triangular commutative diagram and give the necessary condition of the coknernel and coproduct. Furthermore, if C is an additive category, then so is C~â—‡.