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May 31, 2023 at 13:16 answer added Tyler Lawson timeline score: 5
May 31, 2023 at 6:35 history edited Fernando Muro CC BY-SA 4.0
added 16 characters in body; edited title
May 31, 2023 at 6:30 comment added Fernando Muro The problem is that the composite $R_1\to R_3$ must then be zero and, assuming you mean unital $E_\infty$-algebras, that implies that $R_3=0$ so $R_1\to R_2$ is an equivalence and you do get a homotopy fibre sequence in $K$-theory, but a trivial one.
May 31, 2023 at 1:28 history asked user145752 CC BY-SA 4.0