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\begin{document}

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\section*{relaxed multicategory}

\hypertarget{relaxed_multicategories}{}\section*{{Relaxed multicategories}}\label{relaxed_multicategories}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{sketch_of_a_definition}{Sketch of a definition}\dotfill \pageref*{sketch_of_a_definition} \linebreak
\noindent\hyperlink{literature}{Literature}\dotfill \pageref*{literature} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

Vertex algebras are intuitively analogues of associative algebras, except that certain singularities come up (in physics terminology thsi comes from [[OPE]]`s).

Relaxed multicategories can be thought of, according to Borcherds, as multicategories in which the morphisms may have some sort of singularity. In the language of pseudotensor categories (a variant of coloured operads) this is studied by Beilinson and Drinfeld. In connection to quantum groups this has been studied by Soibelman.

\hypertarget{sketch_of_a_definition}{}\subsection*{{Sketch of a definition}}\label{sketch_of_a_definition}

Let $T$ be the free [[monoid]] [[monad]] on [[Set]] and $T^+$ the monad induced by the adjunction of the [[forgetful functor]] from $T$-multicategories to $T$-graphs. Leinster defines a particular $T^+$-multicategory (see [[generalized multicategory]]) $V$. A \textbf{relaxed multicategory} is any $V$-[[enriched multicategory|enriched]] $T$-multicategory.

\hypertarget{literature}{}\subsection*{{Literature}}\label{literature}

\begin{itemize}%
\item [[Tom Leinster]], \emph{Generalized enrichment for categories and multicategories}, \href{http://arxiv.org/abs/math/9901139}{math.QA/9901139}, chapter 4


\item [[Yan Soibelman]], \emph{Meromorphic tensor categories}, \href{http://arxiv.org/abs/q-alg/9709030}{q-alg/9709030}; \emph{The meromorphic braided categroy arising in quantum affine algebras}, \href{http://arxiv.org/abs/math/9901003}{math.QA/9901003}


\item Craig T. Snydal, \emph{Relaxed multi category structure of a global category of rings and modules}, \href{http://arxiv.org/abs/math/9912075}{math.CT/9912075}


\item Craig T. Snydal, \emph{Equivalence of Borcherds G-vertex algebras and axiomatic vertex algebras}, \href{http://arxiv.org/abs/math/9904104}{math.QA/9904104}


\item [[A. A. Beilinson]], [[V. Drinfeld]], \emph{Chiral Algebras}, AMS 2004 (a preprint in various forms since around 1995, cf. \href{http://www.math.uchicago.edu/~mitya/langlands.html}{here}).



\end{itemize}
[[!redirects relaxed multicategory]] [[!redirects relaxed multicategories]]



\end{document}