Completions of Grothendieck groups
Category Theory
2014-02-26 v2 Representation Theory
Abstract
For a certain class of abelian categories, we show how to make sense of the "Euler characteristic" of an infinite projective resolution (or, more generally, certain chain complexes that are only bounded above), by passing to a suitable completion of the Grothendieck group. We also show that right-exact functors (or their left-derived functors) induce continuous homomorphisms of these completed Grothendieck groups, and we discuss examples and applications coming from categorification.
Keywords
Cite
@article{arxiv.1105.2715,
title = {Completions of Grothendieck groups},
author = {Pramod N. Achar and Catharina Stroppel},
journal= {arXiv preprint arXiv:1105.2715},
year = {2014}
}
Comments
13 pages; corrected a mistake in the previous version