Equivalences in Bicategories

Document Type : Research Paper

Author

Department of Mathematics, Universit'e Choua"ib Doukkali, El Jadida, Morocco.

10.29252/cgasa.8.1.19

Abstract

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.

Keywords


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