Reshaping limit diagrams and cofinality in higher category theory

Abstract

We present some results on (co)limits of diagrams in $\infty$-categories, as well as those in $(n,1)$-categories. In particular, we deduce a way to reshape colimit diagrams into simplicial ones, and a characterisations of $n$-cofinality for functor between $\infty$-categories. Some basics on $n$-siftedness are also briefly treated.

21 pages, with correction and addition; reshaped a bit (mainly in sections 5,6,7). Comments are welcome