TY - JOUR ID - 39393 TI - Equivalences in Bicategories JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Abbad, Omar AD - Department of Mathematics, Universit\'e Choua\"ib Doukkali, El Jadida, Morocco. Y1 - 2018 PY - 2018 VL - 8 IS - 1 SP - 19 EP - 33 KW - Equivalences KW - bicategories KW - 1-cells equivalence DO - 10.29252/cgasa.8.1.19 N2 - In 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. UR - https://cgasa.sbu.ac.ir/article_39393.html L1 - https://cgasa.sbu.ac.ir/article_39393_332fddb8a87abd60e8a8e0ea8a4acb90.pdf ER -