Skip to main content
MathOverflow

Return to Answer

added 50 characters in body
Source Link
John Rognes
John Rognes
  • 9.3k
  • 45
  • 52

A published reference for the claim (right after the question in boldface) is the proof given by Thomason on pages 1657-1658 of "First quadrant spectral sequences in algebraic K-theory via homotopy colimits", Comm. Algebra 10 (1982), no. 15, 1589–1668. He shows that if the translations are faithful, then S^{-1} S is equivalent to the mapping cone of the diagonal functor S --> S x S, and that this provides a group completion of S. Baas-Dundas-Richter-R. reviewed this in Lemma 6.2 of our paper on Ring completion of rig categories (Crelle, 2013), where we extend the story to the bimonoidal case.

A published reference for the claim (right after the question in boldface) is the proof given by Thomason on pages 1657-1658 of "First quadrant spectral sequences in algebraic K-theory via homotopy colimits", Comm. Algebra 10 (1982), no. 15, 1589–1668. He shows that if the translations are faithful, then S^{-1} S is equivalent to the mapping cone of the diagonal functor S --> S x S, and that this provides a group completion of S. Baas-Dundas-Richter-R. reviewed this in Lemma 6.2 of our paper on Ring completion of rig categories (Crelle, 2013).

A published reference for the claim (right after the question in boldface) is the proof given by Thomason on pages 1657-1658 of "First quadrant spectral sequences in algebraic K-theory via homotopy colimits", Comm. Algebra 10 (1982), no. 15, 1589–1668. He shows that if the translations are faithful, then S^{-1} S is equivalent to the mapping cone of the diagonal functor S --> S x S, and that this provides a group completion of S. Baas-Dundas-Richter-R. reviewed this in Lemma 6.2 of our paper on Ring completion of rig categories (Crelle, 2013), where we extend the story to the bimonoidal case.

edited body
Source Link
John Rognes
John Rognes
  • 9.3k
  • 45
  • 52

A published reference for the claim (right after the question in boldface) is the proof given by Thomason on pages 1657-1658 of "First quadrant spectral sequences in algebraic K-theory via homotopy colimits", Comm. Algebra 10 (1982), no. 15, 1589–1668. He shows that if the translations are faithful, then S^{-1} S is equivalent to the mapping cone of the diagonal functor S --> S x S, and that this provides a group completion of S. Baas-Dundas-Richter-R. reviewed this in Lemma 6.12 of our paper on Ring completion of rig categories (Crelle, 2013).

A published reference for the claim (right after the question in boldface) is the proof given by Thomason on pages 1657-1658 of "First quadrant spectral sequences in algebraic K-theory via homotopy colimits", Comm. Algebra 10 (1982), no. 15, 1589–1668. He shows that if the translations are faithful, then S^{-1} S is equivalent to the mapping cone of the diagonal functor S --> S x S, and that this provides a group completion of S. Baas-Dundas-Richter-R. reviewed this in Lemma 6.1 of our paper on Ring completion of rig categories (Crelle, 2013).

A published reference for the claim (right after the question in boldface) is the proof given by Thomason on pages 1657-1658 of "First quadrant spectral sequences in algebraic K-theory via homotopy colimits", Comm. Algebra 10 (1982), no. 15, 1589–1668. He shows that if the translations are faithful, then S^{-1} S is equivalent to the mapping cone of the diagonal functor S --> S x S, and that this provides a group completion of S. Baas-Dundas-Richter-R. reviewed this in Lemma 6.2 of our paper on Ring completion of rig categories (Crelle, 2013).

Source Link
John Rognes
John Rognes
  • 9.3k
  • 45
  • 52

A published reference for the claim (right after the question in boldface) is the proof given by Thomason on pages 1657-1658 of "First quadrant spectral sequences in algebraic K-theory via homotopy colimits", Comm. Algebra 10 (1982), no. 15, 1589–1668. He shows that if the translations are faithful, then S^{-1} S is equivalent to the mapping cone of the diagonal functor S --> S x S, and that this provides a group completion of S. Baas-Dundas-Richter-R. reviewed this in Lemma 6.1 of our paper on Ring completion of rig categories (Crelle, 2013).