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${}_{i}$*.

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 $(-) \otimes^{\mathbb{L}} A$ |

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