Under the basic assumptions on generators of backward stochastic differential equations

the one-to-one correspondence between subadditivity (resp. homogeneity) of g-expectations and generators of backward stochastic differential equations is obtained. Thus it is proved that the definitions of dynamic coherent risk measures in Detlefsen-Scandolo (2005) and Jiang (2008) are completely same under the framework of g-expectations. Furthermore

the relationship between time-consistent dynamic coherent risk measures via g-expectations and sublinearity of g-expectations is established.