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A differential graded category is a category enriched over complexes of modules for some commutative ring.

3 votes
0 answers
197 views

On homotopically inverting maps in DG categories

In a DG category $\mathcal{C}$, call a (closed degree 0) morphism $f: X \to Y$ a homotopy equivalence, if there exists $g: Y \to X$ such that $gf-1_X$ and $fg-1_Y$ are exact. For a full DG subcatego …
Dasha Poliakova's user avatar
7 votes
0 answers
143 views

DG functors along which contractions can be lifted

For an object $X$ in a DG category, its contraction is $r \in Hom^{-1}(X,X)$ such that $d(r)=1_X$. Let us say that contractions lift along a DG functor $F: \mathcal{C} \to \mathcal{D}$, if for a contr …
Dasha Poliakova's user avatar