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I am a novice to biblatex and I am a bit confused about the style/citestyle notion. For example, I would like to use the nature bibliography style but with the numeration replaced by the alphabetic style. Of course, I can set style=nature and citestyle=alphabetic, but as far as I see the citestyle really only changes the way the citations appear in the text and not the way the individual entries in the bibliography are designated. Do I need to define a custom style for this?

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You are almost there. You just need to modify the bibliography style a bit to see the alphabetic labels.

The citation and bibliography styles are independent. That means that the bibliography styles do not know which citation style is active. So the bibliography styles based on a numeric style will always give numbers in the bibliography, those based on alphabetic will give alphabetic labels. If you change the citation style in a way that changes the kind of label used for citations, the bibliography style may need to be changed.

\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}

\usepackage[style=nature, citestyle=alphabetic, backend=biber]{biblatex}

\defbibenvironment{bibliography}
  {\list
     {\printtext[labelalphawidth]{%
        \printfield{labelprefix}%
        \printfield{labelalpha}%
        \printfield{extraalpha}}}
     {\setlength{\labelwidth}{\labelalphawidth}%
      \setlength{\leftmargin}{\labelwidth}%
      \setlength{\labelsep}{\biblabelsep}%
      \addtolength{\leftmargin}{\labelsep}%
      \setlength{\itemsep}{\bibitemsep}%
      \setlength{\parsep}{\bibparsep}}%
      \renewcommand*{\makelabel}[1]{##1\hss}}
  {\endlist}
  {\item}

\addbibresource{biblatex-examples.bib}

\begin{document}
\cite{sigfridsson}
\printbibliography
\end{document}

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