All Questions
Tagged with dg-categories differential-graded-algebras
8 questions
3
votes
0
answers
242
views
Wrong way Poincare duality for Calabi-Yau dg-algebras?
Let $A$ be a smooth compact Calabi-Yau dg $k$-algebra of dimension $w$. It is widely known (e.g. Atsusi Takahashi proposition 2.4) that in such situation we have non canonical isomorphism of $A^{en}$-...
- 1,307
3
votes
0
answers
106
views
Explicit description of periodic map $S : HC_{i} \to HC_{i-2}$ for dg and $A_\infty$ algebras
Let $A$ some associative unital $k$-algebra, let $HC_*(A)$ is cyclic homology of $A$ and $HH_*(A)$ is hochschild homology of $A$. Then we have Connes exact sequence:
$$ ... \xrightarrow[]{} HH_n(A) \...
- 1,307
10
votes
0
answers
372
views
Simple question about DG-algebras
Considering the following conditions for two DG-algebras $A$ and $B$:
1) There exists quasi-isomorphic DG-algebra morphism $A \to B$.
2) There exists a DG-algebra $C$ and two quasi-isomorphic DG-...
- 5,562
2
votes
1
answer
175
views
Why do some literatures prefer right module to left module when dealing with DG modules?
I've been trying to read some papers on differential graded modules (for example, Keller, Deriving DG categories)
In most of literature I found about dg-modules, they define them as right modules (Of ...
- 233
10
votes
1
answer
713
views
Why do the model structures on dg-algebras and on dg-categories are not compatible?
First we talk about dg-algebras. According to this n-lab page, we write $dgAlg$ for the category of cochain dg-algebras in non-negative degree over a field $k$ of characteristic $0$. Write $CdgAlg\...
- 9,009
6
votes
1
answer
541
views
Matrix factorizations as a dg-category?
Matrix factorizations (in the graded case) give a triangulated category. I would imagine that there should be an underlying dg-category. Is there such a definition, and if so, where can I find it in ...
- 5,186
2
votes
2
answers
227
views
Does semi-free behave well under totalization
Suppose I have a dg algebra $(A,d)$ and a chain complex $M^\bullet$ of semi-free $(A,d)$ modules. I am hoping it is true that $ Tot^\coprod (M^\bullet)$ is again a semi-free $(A,d)$ module. Is this so?...
- 595
7
votes
1
answer
1k
views
dg objects: Z-graded vs. Z/2Z-graded
I am wondering: Are there any general theorems or principles relating the theory of Z-graded dg objects and the theory of Z/2Z-graded dg objects? I am mainly interested in dg algebras, dg Lie algebras,...
- 21k