Free algebras through Day convolution
Algebraic Topology
2023-02-15 v2 Category Theory
Abstract
Building on the foundations in our previous paper, we study Segal conditions that are given by finite products, determined by structures we call cartesian patterns. We set up Day convolution on presheaves in this setting and use it to give conditions under which there is a colimit formula for free algebras and other left adjoints. This specializes to give a simple proof of Lurie's results on operadic left Kan extensions and free algebras for symmetric -operads.
Keywords
Cite
@article{arxiv.2006.08269,
title = {Free algebras through Day convolution},
author = {Hongyi Chu and Rune Haugseng},
journal= {arXiv preprint arXiv:2006.08269},
year = {2023}
}
Comments
37 pages, v2: Various minor corrections