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\def\calR{{\mathcal R}}

\def\CD{\text{\it CD}}
\def\SMC{\text{\it SMC}}

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\begin{document}
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{\LARGE\bf Cheat Sheet $\CD_a$}
\quad{\red(with Travis Ens)}
\hfill
\parbox[b]{2.5in}{\tiny
  \null\hfill\url{http://drorbn.net/AcademicPensieve/People/Ens/}
  \newline\null\hfill
   created May 8, 2019, last modified \today
}

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\begin{multicols}{2}

{\bf Notation.} $id_1=\II$, $id_2=\III$, $d_0D=\II\vdash D$, $d_\infty D=D\vdash\II$.

{\bf Theorem.} As strict monoidal categories enriched over graded algebras, ${\CD_a = \SMC\langle \H,\IX\mid\calR\rangle}$\footnote{$\IX$ is \texttt{\symbol{92}mathrm\string{\symbol{92}mathsf\string{IX\string}\string}}.}, where $\deg(\H,\IX)=(1,0)$ and where $\calR$ is generated by:

\begin{itemize}[leftmargin=*,labelindent=0pt,itemsep=-4pt,topsep=0pt]
\item Idempotency: $(\IX)^2=id_2$.
\item Flat R3: ${(\IX\vdash\II)(\II\vdash\IX)(\IX\vdash\II) = (\II\vdash\IX)(\IX\vdash\II)(\II\vdash\IX)}$
\item Chord Flip: $[d_0\H+\IH,\IX]=0$.
\end{itemize}
\[ \input{figs/Relations.pdf_t} \]

\end{multicols}

\[ \includegraphics[width=\textwidth]{SyzygiesCheetSheet-180708-bottom.jpg} \]

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