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Results tagged with dg-categories
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user 29322
A differential graded category is a category enriched over complexes of modules for some commutative ring.
2
votes
1
answer
350
views
Are dg-modules over a cofibrant dg-category cofibrant?
Fix a commutative ring $k;$ all dg-categories will be dg-categories over $k.$ Throughout the question, I will be following the notation and conventions of Toën's "The homotopy theory of dg-categories …
- 1,349
9
votes
0
answers
436
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Symmetric monoidal structure(s) on the $\infty$-category of dg-categories
Let $k$ be a commutative ring with $1$, and let $\mathsf{dgCat}_k$ be the category of $k$-linear dg-categories, as defined in [1, Section 2]. We may equip $\mathsf{dgCat}_k$ with the Morita model stru …
- 1,349
3
votes
0
answers
170
views
(Commutative) Algebras in $\mathsf{dgCat}_k$
Suppose $k$ is a fixed commutative ring, and let $\mathsf{dgCat}_k$ denote the category of $k$-linear dg-categories. We will equip $\mathsf{dgCat}_k$ with the Morita model structure (see theorem 2.27 …
- 1,349
8
votes
0
answers
466
views
Relationship between different definitions of the Hochschild homology
Throughout the literature, one can find many definitions of the Hochschild homology of various objects. However, the precise relationship between these definitions is not always so clear, at least to …
- 1,349