Quandle cohomology is a Quillen cohomology
Copyright policy )Quandle cohomology is a Quillen cohomology
Racks and quandles are fundamental algebraic structures related to the topology of knots, braids, and the Yang–Baxter equation. 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. 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).
quandles, Knot theory, Abstract and axiomatic homotopy theory in algebraic topology, Mathematics - Category Theory, K-Theory and Homology (math.KT), Other homology theories in algebraic topology, Quillen homology, racks, Nonabelian homological algebra (category-theoretic aspects), quandle cohomology, flat base change, Mathematics - K-Theory and Homology, Mathematics - Quantum Algebra, FOS: Mathematics, Algebraic Topology (math.AT), Quantum Algebra (math.QA), Category Theory (math.CT), Mathematics - Algebraic Topology, transitivity, Sets with a single binary operation (groupoids)
quandles, Knot theory, Abstract and axiomatic homotopy theory in algebraic topology, Mathematics - Category Theory, K-Theory and Homology (math.KT), Other homology theories in algebraic topology, Quillen homology, racks, Nonabelian homological algebra (category-theoretic aspects), quandle cohomology, flat base change, Mathematics - K-Theory and Homology, Mathematics - Quantum Algebra, FOS: Mathematics, Algebraic Topology (math.AT), Quantum Algebra (math.QA), Category Theory (math.CT), Mathematics - Algebraic Topology, transitivity, Sets with a single binary operation (groupoids)
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