Soft categories

In this thesis study, at first the category of soft sets and soft functions is defined by using the definition of soft function and this category is sembolized by SFun. Soft monomorphism and soft epimorphism are defined for SFun categorical structure and some properties are obtained dealing with these soft morphisms. Afterwards, soft section is defined and the connection between soft section and soft monomorphism is stated. Moreover definiton of soft retraction is given and the connection between soft retraction and soft epimorphism is obtained. By defining soft isomorphism some theorem and prepositions which state the connections between soft monomorphism, soft epimorphism, soft retraction and soft section are obtained and proved. Initial and terminal objects are defined for the category SFun and it is proved that this objects are unique up to soft isomorphism. Finally, zero object is defined for the category SFun and some properties are stated for the category SFun which has zero object.