Completions of Grothendieck groups

Details Completions of Grothendieck groups Completions of Grothendieck groups

2011-05-13

arxiv.org/abs/1105.2715v2

Mathematics

Category Theory

13 pages; corrected a mistake in the previous version

Scientific paper

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.

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