nLab derived tensor product

Idea

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

Examples

• Tor

• symmetric monoidal smash product of spectra

Related concepts

	homotopy	cohomology	homology
	$[S^n,-]$	$[-,A]$	$(-) \otimes A$
category theory	covariant hom	contravariant hom	tensor product
homological algebra	Ext	Ext	Tor
enriched category theory	end	end	coend
homotopy theory	derived hom space $\mathbb{R}Hom(S^n,-)$	cocycles $\mathbb{R}Hom(-,A)$	derived tensor product $(-) \otimes^{\mathbb{L}} A$