Wobbly double functors (Q2017478)

The paper continues the study of double categories and functors started by the author together with \textit{M. Grandis} [Cah. Topol. Géom. Différ. Catég. 40, 162--220 (1999; Zbl 0939.18007); Cah. Topol. Géom. Différ. Catég. 45, No. 3, 193--240 (2004; Zbl 1063.18002)]. The notion of (co)lax wobbly double functor is introduced. It is shown that the adjointness between lax and colax wobbly double functors (Theorem 2.8) and weak equivalence of double categories (Theorem 3.1) may be easily treated in the terms of underlying ordinary functors.