In this project, we proved that we can write any permutation in the form of product of (n-1,1)*(n-2,1)*(n-3,1)*...* (1,1)$ shuffles , and we are currently exploring how one can define an analogue of the endomorphism operads for Tate objects by considering all of its tensor products. We have already constructed Ev(n), which is the endomorphism operad produced by tensor product of Tate objects, and an explicit map of Ev(2). Then we defined a general composition operator and we would like to further explore its structure.