Previdi's delooping conjecture for exact categories
Previdi's delooping conjecture for exact categories
Let be an exact category. Write for the geometric realization of the simplicial category given by Waldhausen's -construction. The category is partially abelian if it and its opposite have pullbacks of admissible monomorphisms with common target. Write for Beilinson's category of generalized Tate objects associated to . The homotopy groups of the loop space of are the algebraic -theory groups of . Previdi's delooping conjecture. If is partially abelian, then is delooped by . This conjecture proposes a delooping relation between the Waldhausen space of an exact category and that of its category of generalized Tate objects; the paper's abstract says that it proves a modified version using non-connective -theory spectra, so the precise original formulation should be checked against that modification.
Sources & referencesView supporting material
Primary source
Sho Saito, “On Previdi's delooping conjecture for K-theory”, arXiv:1203.0831 (2013).
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