Quandle cohomology is a Quillen cohomology

Abstract

We show that the cohomology groups usually associated with racks and quandles agree with the Quillen cohomology groups for the algebraic theories of racks and quandles, respectively. We also explain how this makes available the entire range of tools that comes with a Quillen homology theory, such as long exact sequences (transitivity) and excision isomorphisms (flat base change).

27 pages, to appear in Trans. Amer. Math. Soc

Cited by in corpus (7)

• Quandle cohomology, extensions and automorphisms
• The homotopy types of free racks and quandles
• Zero-divisors and idempotents in quandle rings
• On homology of Lie algebras over commutative rings
• Groups, conjugation and powers
• The homology of permutation racks
• Derivations of quandles