Timeline for What is the correct definition of the (derived) tensor product over a dg-algebra?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2013 at 18:48 | answer | added | tujunwu | timeline score: 2 | |
| Nov 11, 2013 at 15:27 | comment | added | Kevin Walker | Is it possible that the example you are interested can be interpreted as some sort of dual to a derived tensor product (which would convert the standard direct sums into direct products)? | |
| Nov 11, 2013 at 14:40 | comment | added | Daniel Pomerleano | More specifically look at page 18. | |
| Nov 11, 2013 at 14:02 | comment | added | Daniel Pomerleano | You can look at work of Leonid Positselski for what I think is an extremely detailed discussion of this point: The shortest reference is arxiv.org/pdf/1010.0982v2.pdf and I believe what you are discussing is called "a derived functor of the second kind." I guess the punch line is that there are sort of exotic derived categories of the second kind where the thing you write down is the natural functor. | |
| Nov 11, 2013 at 2:32 | comment | added | Theo Johnson-Freyd | My answer to the question that you did not ask is: carry on, and in the paper call your thing the "completed derived tensor product", and give it a precise definition. Probably best to check that it is reasonably well-behaved, e.g. a homotopy functor in its various variables. | |
| Nov 11, 2013 at 2:15 | comment | added | Qiaochu Yuan | The universal property of the derived tensor product should be about maps coming out of it (e.g. it should be left adjoint to the derived hom, it should preserve homotopy colimits) and that makes sums a natural method of construction while products aren't. | |
| Nov 11, 2013 at 2:13 | answer | added | Peter May | timeline score: 11 | |
| Nov 11, 2013 at 1:32 | history | asked | John Pardon | CC BY-SA 3.0 |