nLab
CommAlg

Definition

$\mathrm{CommAlg}$ or $\mathrm{CAlg}$denotes a category of commutative associative algebras.

Usually this is understood implicitly as algebras over some ground field $k$. In this case

$$\mathrm{CommAlg}\simeq k/\mathrm{CRing}$$CommAlg \simeq k/CRing

is the slice category of CRing – the category of commutative rings – under $k$.

Properties

• Via measure coalgebras $\mathrm{CommAlg}$ is naturally enriched over the category Coalg? of cocommutative coalgebras.

category: category