In this paper we introduce two notions —systems of fibrant objects and fibration structures— which will allow us to associate to a bicategory B a homotopy bicategory Ho(B) in such a way that Ho(B) is the universal way to add pseudo-inverses to weak equivalences in B. Furthermore, Ho(B) is locally small when B is and Ho(B) is a 2-category when B is. We… (More)
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