Functors on Posets Left Kan Extend to Cosheaves: an Erratum
Category Theory
2019-07-23 v1 Algebraic Topology
Abstract
In this note we give a self-contained proof of a fundamental statement in the study of cosheaves over a poset. Specifically, if a functor has domain a poset and co-domain a co-complete category, then the left Kan extension of that functor along the embedding of the domain poset into its poset of down-sets is a cosheaf. This proof is meant to replace the mistaken proofs published in the author's thesis and an article on dualities exchanging cellular sheaves and cosheaves.
Cite
@article{arxiv.1907.09416,
title = {Functors on Posets Left Kan Extend to Cosheaves: an Erratum},
author = {Justin Curry},
journal= {arXiv preprint arXiv:1907.09416},
year = {2019}
}
Comments
10 pages, 1 figure; erratum to thesis and JPAA article