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arXiv · 1111.4262

Grothendieck groups and a categorification of additive invariants

Joerg Schuermann·Shoji Yokura
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Abstract

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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Joerg Schuermann, Shoji Yokura. 2011-11-18. Grothendieck groups and a categorification of additive invariants. https://doi.org/10.1142/s0129167x12500577

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