A Study On Adjoint Pair In N-Angulated Categories

In this paper,we discuss the axioms for an n-angulated category,which is introduced by Geiss,Keller and Oppermann in[15].Bergh and Thaule took it a step further about the composotion of the axioms for pre-n-angulated category in[9],and gave some equivalent statements about axioms.We improve some of their results,and we depict pre-n-angulated category by a weak isomorphism of coexact n-Σ-sequences.On the other hand,we generalize some results about adjoint pair in triangulated categories to n-angulated categories.Firstly,we improve that if(F,G)is an adjoint pair of functors of n-angulated categories,then F is an n-angulated functor if and only if so is G.Secondly,we prove that looking for adjoints to triangulated functors reduces to looking for adjoints to the associated exact functors,which is an extension of Neeman’s result[27].