Timeline for Understanding the higher stack of perfect complexes
Current License: CC BY-SA 4.0
15 events
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| Apr 24, 2021 at 20:46 | history | edited | Martin Hurtado | CC BY-SA 4.0 |
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| Apr 22, 2021 at 21:51 | history | edited | Martin Hurtado | CC BY-SA 4.0 |
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| Apr 18, 2021 at 17:56 | history | edited | Martin Hurtado | CC BY-SA 4.0 |
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| Apr 17, 2021 at 20:19 | comment | added | Denis Nardin | The Dold-Kan correspondence tells you exactly how to build that Kan complex. Then there's a theorem by Quillen that basically tells you that a Kan complex is as good as a topological space for what concerns homotopy type (and in fact I and other homotopy theorists often refer to a Kan complex as a space, and for me the mapping space is defined as a Kan complex) | |
| Apr 17, 2021 at 16:09 | history | edited | Martin Hurtado | CC BY-SA 4.0 |
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| Apr 17, 2021 at 15:53 | comment | added | Martin Hurtado | I guess the Dold-Kan correspondence allows you to pass from the homology groups of the complex that appear in the Ext's in to mapping spaces of the simplicial object but still I dont know the form of this mapping spaces so I cannot see the geometry there (Sorry if say any stupid thing, I am not an expert in homotopy theory/higher category theory) | |
| Apr 17, 2021 at 15:45 | history | edited | Martin Hurtado | CC BY-SA 4.0 |
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| Apr 17, 2021 at 14:56 | comment | added | Martin Hurtado | Sure, I have to think on that to understand the higher homotopy groups of the stack. I am going to rephrase a bit more the question (sorry it is a bit messy) | |
| Apr 17, 2021 at 9:47 | comment | added | Denis Nardin | The key thing you seem to be missing in your intuition is the Dold-Kan correspondence that identifies chain complexes with abelian groups in simplicial sets (i.e. ``spaces''), and their homology groups with the homotopy groups of the underlying simplicial set. | |
| Apr 17, 2021 at 9:13 | history | edited | Martin Hurtado | CC BY-SA 4.0 |
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| Apr 15, 2021 at 18:02 | history | edited | Martin Hurtado | CC BY-SA 4.0 |
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| Apr 15, 2021 at 15:12 | history | edited | Martin Hurtado | CC BY-SA 4.0 |
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| Apr 15, 2021 at 13:06 | comment | added | Martin Hurtado | Sorry, it was a typo. The ">" symbol that appears with the quote command mixed with the own equations symbols a couple of times. I think it is correct now | |
| Apr 15, 2021 at 13:03 | history | edited | Martin Hurtado | CC BY-SA 4.0 |
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| Apr 15, 2021 at 12:40 | history | asked | Martin Hurtado | CC BY-SA 4.0 |