Transfer of Lax and Pseudofunctor structure

DUBUC, EDUARDO J

GENOVA

Congreso; CT20->21; 2021

While cleaning up, fixing errors, and the like, in the bicategorical fibrant-cofibrant \mbox{replacement} developed in a first version of the preprint \cite{DDS}, we realized that what it was actually going on was a transfer of the trivial pseudofunctor structure on the identity functor to the fibrant-cofibrant replacement construction on a model bicategory. We decided to define and develop a general notion of \emph{Transfer of Lax and Pseudo functor structures}, Appendix A in \cite{DDS}, to be applied then in the theory of model bicategories. I will present this notion as an instance of a notion of (iso)fibration 2-functor similar to the notion of \emph{equiv-fibration} in \cite{nL}.