nLab derived tensor product

Contents

Contents

Idea

The left derived functor of a tensor product functor. In the context of triangulated categories denoted by L\stackrel{\mathbf{L}}\otimes or L\otimes^L. In the context of classical homological algebra its components (the classical left derived functors) are traditionally denoted by Tor i{}_{i}.

Examples

homotopycohomologyhomology
[S n,][S^n,-][,A][-,A]()A(-) \otimes A
category theorycovariant homcontravariant homtensor product
homological algebraExtExtTor
enriched category theoryendendcoend
homotopy theoryderived hom space Hom(S n,)\mathbb{R}Hom(S^n,-)cocycles Hom(,A)\mathbb{R}Hom(-,A)derived tensor product () 𝕃A(-) \otimes^{\mathbb{L}} A

Last revised on July 18, 2023 at 13:39:10. See the history of this page for a list of all contributions to it.