Reshaping limit diagrams and cofinality in higher category theory

TL;DR

This paper explores (co)limits in higher categories, providing methods to reshape colimit diagrams, characterizing n-cofinality, and discussing n-siftedness in the context of $ $-categories and $ ext{(n,1)}$-categories.

Contribution

It introduces a new approach to reshape colimit diagrams into simplicial forms and characterizes n-cofinality for functors between $ $-categories.

Findings

Reshaping colimit diagrams into simplicial forms.

Characterization of n-cofinality for functors.

Brief treatment of n-siftedness.

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.