Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58538120180101Equivalences in Bicategories193339393ENOmar AbbadDepartment of Mathematics, Universit\'e Choua\"ib Doukkali, El Jadida, Morocco.Journal Article20160313In this paper, we establish some connections between the concept of an equivalence of categories and that of an equivalence in a bicategory. Its main result builds upon the observation that two closely related concepts, which could both play the role of an equivalence in a bicategory, turn out not to coincide. Two counterexamples are provided for that goal, and detailed proofs are given. In particular, all calculations done in a bicategory are fully explicit, in order to overcome the difficulties which arise when working with bicategories instead of 2-categories.http://cgasa.sbu.ac.ir/article_39393_332fddb8a87abd60e8a8e0ea8a4acb90.pdf