nLab
hom-object

Contents

Idea

An ordinary locally small category CC has for any ordered pair of objects x,yx,y a hom-set C(x,y)C(x,y)—an object in the category $Set$.

For CC more generally an enriched category over a closed monoidal category VV, there is – by definition – for all x,yx,y an object C(x,y)objVC(x,y) \in obj V that plays the role of the “collection of morphisms” from xx to yy

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

Revised on June 29, 2012 02:04:28 by Urs Schreiber (89.204.139.141)