Grothendieck groups and a categorification of additive invariants

Details Grothendieck groups and a categorification of additive invariants Grothendieck groups and a categorification of additive invariants

2011-11-18

arxiv.org/abs/1111.4262v1

Mathematics

Algebraic Geometry

27 pages, to appear in International J. Mathematics

Scientific paper

A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general categorical set-up we introduce a generalized relative Grothendieck group from a cospan of functors of categories and also consider a categorification of additive invariants on objects. As an example, we obtain a general theory of characteristic homology classes of singular varieties.

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