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% $Id: HopfAlgebraWithBasis.tex,v 1.1.1.3 2004/10/04 17:25:13 nthiery Exp $
% File:		lib/DOMAINS/CATEGORY/DOC/HopfAlgebraWithBasis.tex
% Authors:	Nicolas M. Thiéry <nthiery@users.sourceforge.net>
% Purpose:	Documentation for the category Cat::HopfAlgebraWithBasis
% Created:	Wed Sep  3 14:48:49 2003
% License:	LGPL
% Project:	MuPAD-Combinat, http://mupad-combinat.sf.net
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\begin{Mhelppage}{HopfAlgebraWithBasis}{Nicolas M. Thiéry}
  [ImplState=stable,TestState=beta,DocState=stable]
%\Mproofread{...}{...}{...}

\begin{MInfo}
  \eng{the category of Hopf algebras over a distinguished basis}
  \de{}
\end{MInfo}

\Mproofread{nthiery}{22/09/2003}{minimal definition}
\begin{MIntro}
  \eng{\Mthis{} represents the category of Hopf algebras over a
    distinguished basis.}
  \de{}
\end{MIntro}

\begin{MCatConst}
  \MCall{R}
\end{MCatConst}

\begin{MParameters}
  \param{R}
    \eng{A domain which must be from the category \Mex{Cat::Ring}.}
    \de{}
\end{MParameters}

\begin{MCategories}
  \Mupc{Cat::AlgebraWithBasis}{R}
%,\Mupc{Cat::HopfAlgebra}{R}
%,\Mupc{Cat::GradedBialgebraWithBasis}{R}
\end{MCategories}

\begin{MDetails}
  \eng{A \Mthis{} is a Hopf algebra over a distinguished basis. The
    Hopf algebra operations (product, coproduct, counit) are typically
    implemented by extending by linearity their definitions on the basis
    elements.}
  \de{}
\end{MDetails}

%\begin{MDomBasEntries}
%  \MDomEntry{bla}
%  \eng{.}
%  \de{}
%\end{MDomBasEntries}

\begin{MChanges}
  \version{3.0}
  \eng[New category]{\Mthis{} is a new category} %
\end{MChanges}

\end{Mhelppage}
