# Derived tensor product

In algebra, given a differential graded algebra *A* over a commutative ring *R*, the **derived tensor product** functor is

where and are the categories of right *A*-modules and left *A*-modules and *D* refers to the homotopy category (i.e., derived category).[1] By definition, it is the left derived functor of the tensor product functor .

## See also

- derived scheme (derived tensor product gives a derived version of a scheme-theoretic intersection.)

## Notes

- Hinich, Vladimir (1997-02-11). "Homological algebra of homotopy algebras". arXiv:q-alg/9702015.

## References

- Lurie, J.,
*Spectral Algebraic Geometry (under construction)* - Lecture 4 of Part II of Moerdijk-Toen, Simplicial Methods for Operads and Algebraic Geometry
- Ch. 2.2. of Toen-Vezzosi's HAG II

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