1. Labels and Cross-References

Use \label and \ref to reference elements within an article.

1.1. Referencing Theorem Environments

\begin{theorem}[Intermediate Value Theorem]
\label{thm:ivt}
...
\end{theorem}

By Theorem \ref{thm:ivt}...

1.2. Referencing Equations

Label an equation environment and reference it with \eqref:

\begin{equation}
\label{eq:euler}
e^{i\theta} = \cos\theta + i\sin\theta
\end{equation}

Equation \eqref{eq:euler} is known as Euler's formula.

Result:

Equation (1) is known as Euler's formula. Substituting $\theta =\pi$ yields Euler's identity $e^{i\pi }+1=0$.

1.3. Referencing Figures and Tables

\begin{figure}
\centering
\begin{mermaid}
graph LR
    A["label"] --> B["ref"]
    A --> C["eqref"]
    A --> D["cref"]
\end{mermaid}
\caption{Folio's cross-reference commands}
\label{fig:ref-commands}
\end{figure}

Figure \ref{fig:ref-commands} shows the cross-reference commands.

Result:

graph LR
    A["label"] --> B["ref"]
    A --> C["eqref"]
    A --> D["cref"]

Figure 1 shows the cross-reference commands.

1.4. \cref Command

\cref automatically detects the type of referenced element (theorem, equation, figure, etc.) and prepends the name:

\cref{thm:ivt}    % → "Theorem 1" etc.
\cref{eq:euler}    % → "Equation (1)" etc.

2. Links

2.1. URL Links

\url displays the URL as-is and makes it a hyperlink:

\url{https://interconnectd.app}

Result: https://interconnectd.app

2.2. Text Links

\href customizes the link text:

\href{https://interconnectd.app}{Folio's Website}

Result: Folio's Website

2.3. Inter-Article Links

To link to another Folio article, use the article's URL path:

\href{/articles/articleId}{Article Title}

3. Footnotes

Create footnotes with \footnote:

Euler\footnote{Leonhard Euler, 1707--1783} was a Swiss mathematician.

Result: Euler¹ was a Swiss mathematician.

Footnotes are automatically numbered and collected at the bottom of the article. Math can be used inside:

The Gaussian integral² is an important definite integral.

4. Citations

On Folio, register references in the dashboard, and they appear in \cite{} autocomplete across all articles. While BibTeX files are not used, the \cite, \citep, and \citet commands work as expected.

\cite{einstein1905}          % → [1] or (Einstein, 1905) etc.
\citep{knuth1997}            % → Parenthetical citation
\citet{dijkstra1959}         % → Textual citation

Citation style (numeric / author-year / alpha) can be selected in Settings. The reference list is auto-generated at the end of the article.

5. Custom Commands in Detail

On Folio, registering \newcommand and other macro definitions in the Settings preamble editor applies them to all articles automatically. No per-article preamble needed. Of course, commands used only in a specific article can be written directly in that article.

5.1. Basic \newcommand

% No arguments
\newcommand{\R}{\mathbb{R}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\N}{\mathbb{N}}

% One argument
\newcommand{\abs}[1]{\left| #1 \right|}
\newcommand{\norm}[1]{\left\| #1 \right\|}

% Two arguments
\newcommand{\inner}[2]{\left\langle #1, #2 \right\rangle}
\newcommand{\set}[2]{\left\{ #1 \mid #2 \right\}}

After registration, \abs{x} expands to $\left|x\right|$, and \set{x \in \mathbb{R}}{\abs{x} < 1} expands to $\left\{x\in \mathbb{R}\mid \left|x\right|<1\right\}$.

5.2. \DeclareMathOperator

Define standard mathematical function names:

\DeclareMathOperator{\tr}{tr}       % Trace
\DeclareMathOperator{\rank}{rank}   % Rank
\DeclareMathOperator{\Hom}{Hom}     % Homomorphism set
\DeclareMathOperator{\End}{End}     % Endomorphisms
\DeclareMathOperator{\Aut}{Aut}     % Automorphisms
\DeclareMathOperator{\Im}{Im}       % Image
\DeclareMathOperator{\Ker}{Ker}     % Kernel

This gives proper roman font: $\mathrm{Hom}(G,H)$ and $\mathrm{Aut}(G)$.

5.3. \def Command

For simple macros, \def also works:

\def\eps{\varepsilon}

After registration, \eps expands to $\epsilon$. Example: For any $\epsilon >0$...

6. List Environments in Detail

6.1. Nested Lists

Lists can be nested:

\begin{enumerate}
\item Group theory fundamentals
  \begin{itemize}
  \item Group axioms
  \item Subgroups
  \item Normal subgroups
  \end{itemize}
\item Linear algebra fundamentals
  \begin{itemize}
  \item Vector spaces
  \item Linear maps
  \item Eigenvalues and eigenvectors
  \end{itemize}
\end{enumerate}

Result:

1. Group theory fundamentals

   • Group axioms

   • Subgroups

   • Normal subgroups

2. Linear algebra fundamentals

   • Vector spaces

   • Linear maps

   • Eigenvalues and eigenvectors

6.2. description Environment

An environment suited for terminology explanations:

\begin{description}
\item[\texttt{theorem}] An environment for mathematical theorems.
\item[\texttt{definition}] An environment for mathematical definitions.
\item[\texttt{proof}] An environment for proofs.
\end{description}

Result:

theorem

An environment for mathematical theorems. The body is displayed in italic.

definition

An environment for mathematical definitions. The body is displayed in roman.

proof

An environment for proofs. A QED symbol is appended automatically.

7. Alignment and Layout

7.1. centering

\begin{center}
Centered text
\end{center}

7.2. Box Commands

Use \fbox to enclose text in a box:

\fbox{Boxed text}

Result:

Boxed text

8. Summary

In this article, we covered cross-references (\label/\ref), links (\url/\href), footnotes (\footnote), custom commands (\newcommand/\DeclareMathOperator), list environments, and layout commands on Folio.

This concludes the "Folio Basics" series. For a quick-reference overview of all features, see the "Folio LaTeX Reference" article.