I am studying the notion of the cotangent complexes of Artin stacks reading LMB's book and Olsson's paper. According to them, the cotangent complexes are defined as projective systems in their derived category.

However, in Lemma 2.1 and Proposition 2.2 of Zhang's paper(https://arxiv.org/pdf/1111.6294), the cotangent complexes of Artin stacks are elements of their derived category, where we consider their lisse-etale sites. 

Is this correct ?  (Did the author take the limit?)
 I am confused...

Any comment welcome! Thank you!