Timeline for Lift chain complex from $\mathbb{F}_2$ to $\mathbb{Z}$
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| May 20, 2014 at 9:10 | vote | accept | Sucharit Sarkar | ||
| May 19, 2014 at 17:27 | comment | added | Qiaochu Yuan | @Pasha: every chain complex over a field is isomorphic to a chain complex in which every differential is the composition of a projection out of a direct sum and an inclusion into another direct sum. To lift an object $d$ in a category $d \in D$ through a functor $F : C \to D$ is to find an object $c \in C$ such that $F(c) \cong d$. In this case $C, D$ are chain complexes over $\mathbb{Z}$ and $\mathbb{F}_2$ respectively and $F$ is tensor with $\mathbb{F}_2$. $0$ refers to a matrix entry and not to an object. | |
| May 19, 2014 at 16:01 | answer | added | David E Speyer | timeline score: 13 | |
| S May 19, 2014 at 13:44 | history | suggested | Marco Golla | CC BY-SA 3.0 |
I've edited all occurrences of $F_2$ and $Z$ to improve readability, and added the chain-complexes tag.
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| May 19, 2014 at 13:37 | review | Suggested edits | |||
| S May 19, 2014 at 13:44 | |||||
| May 19, 2014 at 13:25 | history | edited | Sucharit Sarkar | CC BY-SA 3.0 |
added 28 characters in body
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| May 18, 2014 at 11:42 | comment | added | Pasha Zusmanovich | 1. What is "the structure theorem for chain complexes over F_2"? 2. What does it mean "lift"? I understand it as lifting in the category of vector spaces, so 0 should go to 0 automatically, isn't it? | |
| Apr 14, 2014 at 21:20 | history | edited | Sucharit Sarkar | CC BY-SA 3.0 |
Added clarifications in response to comments.
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| Apr 14, 2014 at 21:02 | comment | added | Noah Stein | @LeeMosher: I took $F_2$ to mean the field of two elements here. | |
| Apr 14, 2014 at 20:50 | comment | added | Lee Mosher | What is $F_2$? If it is the free group of rank $2$, which is what that notation means to me, then what is a chain complex over $F_2$ given that $F_2$ is a nonabelian group? | |
| Apr 14, 2014 at 16:39 | comment | added | Włodzimierz Holsztyński | It'd be a pleasure to consider this topic, but personally I would prefer much more explicit definitions. It'd be perhaps a couple of extra lines, and things would be clearer to me. | |
| Apr 14, 2014 at 15:50 | review | First posts | |||
| Apr 14, 2014 at 15:51 | |||||
| Apr 14, 2014 at 15:31 | history | asked | Sucharit Sarkar | CC BY-SA 3.0 |