Counit

The counit $\varepsilon$: picks out the coefficient of the empty composition, the degree-0 part of element.

WikipediaHopf algebra↗MathWorldHopfAlgebra↗WikidataQ1627597↗Encyclopedia of MathematicsHopf_algebra↗nLabHopf algebra↗

Counit(element)$\varepsilon(\text{element})$

Typed signatures

Type	Package	Applies
(number) -> integer	hopf	always

Domain: Hopf algebras

Plot

Examples

Basic #

The empty composition has coefficient $1$

live ↗

In$\mathrm{Counit}(\mathrm{NSymH}(\bigl\lbrack\bigr\rbrack))$Out$1$

Positive degree is sent to $0$

live ↗

In$\mathrm{Counit}(\mathrm{NSymH}(\bigl\lbrack2\bigr\rbrack))$Out$0$

About

Examples	2
Crosswalk	WikipediaMathWorldWikidataEncyclopedia of MathematicsnLab

See also: Coproduct, Antipode