Feysal Hassani - Department of Mathematics, Payame Noor University (PNU), P. OBox, ۱۹۳۹۵-۴۶۹۷ Tehran, Iran
Samira Hashemi - Department of Mathematics, Payame Noor University (PNU), P. OBox, ۱۹۳۹۵-۴۶۹۷ Tehran, Iran
Rasul Rasuli - Department of Mathematics, Payame Noor University (PNU), P. OBox, ۱۹۳۹۵-۴۶۹۷ Tehran, Iran

In this paper, the concepts of n-monomorphism, n-epimorphism, n-isomorphism, n-equivalent, n-coproduct, n-product, n-injection, n-projection, n-initial object, n-terminal object, n-pushout diagram, n-inverse system, n-inverse limit, and n-homology of categories will be introduced and will be shown the relationship between them. Next, some of their properties and structure characteristics will be investigated and obtained some results about them.

Category theory, n-projective and n-injective objects, n-homomorphisms, n-epimorphisms and n-monomorphisms, n-limits, n-colimits, n-ker and n-coker