For bifibrations in small categories, the length of cup products in the kernel of an induced Baues-Wirsching cohomology map lower-bounds the Svarc genus.
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Baues-Wirsching Cohomology and Svarc Genus in Small Categories
For bifibrations in small categories, the length of cup products in the kernel of an induced Baues-Wirsching cohomology map lower-bounds the Svarc genus.