Timeline for Example of non-saturated (co)fibration category
Current License: CC BY-SA 4.0
6 events
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| Feb 10, 2021 at 14:52 | comment | added | Connor Malin | @ReidBarton Good point; if you expand to allow homotopy equivalences with zero torsion, then we do get the two-out-of-three condition. I'm not sure how it affects the various pushout properties. Probably is an explicit computation using cell decompositions. | |
| Feb 10, 2021 at 14:35 | comment | added | Tim Campion | @ReidBarton Oh gosh -- thinking back, this has been an endless source of confusion to me. It's widely known that simple homotopy equivalences give a good example of "equivalence-like maps" which don't have all the properties you'd expect, but exactly which properties they fail to have -- 2/3? 2/6? saturation? is something I have never been 100% sure of. Perhaps part of the issue is that it depends on exactly which category / which weak equivalences of the "simple" flavor you're talking about? | |
| Feb 10, 2021 at 14:12 | comment | added | Reid Barton | Thanks, this is an interesting example. However, I think it's not quite what I'm looking for, because the simple maps do not satisfy the two-out-of-three condition either. I'll edit the question to clarify what I mean by a cofibration category. | |
| Feb 7, 2021 at 20:31 | comment | added | John Rognes | ... and this notion of weak equivalence (simple maps) is a relevant one because it leads to Hatcher's Higher simple homotopy theory and Waldhausen's stable parametrized h-cobordism theorem, connecting the algebraic K-theory of spherical group rings to h-cobordism spaces, concordance/pseudoisotopy spaces and automorphism groups of manifolds | |
| Feb 7, 2021 at 20:22 | history | edited | John Rognes | CC BY-SA 4.0 |
added link to book reference
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| Feb 7, 2021 at 18:06 | history | answered | Connor Malin | CC BY-SA 4.0 |