On K1 of an assembler
Copyright policy )On K1 of an assembler
This paper contains a construction of generators and partial relations for $K_1$ of a simplicial Waldhausen category where cofiber sequences split up to weak equivalence. The main application of these generators and relations is to produce generators for $K_1$ of a (simplicial) assembler.
25 pages
spectra, Simplicial sets; simplicial objects in a category, Stable homotopy theory, spectra, algebraic K-theory, K-Theory and Homology (math.KT), Nonabelian homotopical algebra, assembler, Whitehead groups and \(K_1\), 19D99, 18F30, 14C35, 14E07, Waldhausen categories, Mathematics - K-Theory and Homology, FOS: Mathematics, Grothendieck groups (category-theoretic aspects), Algebraic Topology (math.AT), Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Grothendieck topologies and Grothendieck topoi, Mathematics - Algebraic Topology, Dissections and valuations (Hilbert's third problem, etc.)
spectra, Simplicial sets; simplicial objects in a category, Stable homotopy theory, spectra, algebraic K-theory, K-Theory and Homology (math.KT), Nonabelian homotopical algebra, assembler, Whitehead groups and \(K_1\), 19D99, 18F30, 14C35, 14E07, Waldhausen categories, Mathematics - K-Theory and Homology, FOS: Mathematics, Grothendieck groups (category-theoretic aspects), Algebraic Topology (math.AT), Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Grothendieck topologies and Grothendieck topoi, Mathematics - Algebraic Topology, Dissections and valuations (Hilbert's third problem, etc.)
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