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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeMay 10th 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexCreated [[cartesian multicategory]].

   Created cartesian multicategory.

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeMay 13th 2012
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexNice!

   Nice!

3. • CommentRowNumber3.
   • CommentAuthorSam Staton
   • CommentTimeJun 11th 2021
   • PermaLink
   Author: Sam Staton
   Format: MarkdownItexAlternative presentation along the lines of abstract clones. Hope I got this right, I'm not sure of a reference. <a href="https://ncatlab.org/nlab/revision/diff/cartesian+multicategory/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/cartesian+multicategory/7">v7</a>, <a href="https://ncatlab.org/nlab/show/cartesian+multicategory">current</a>

   Alternative presentation along the lines of abstract clones. Hope I got this right, I’m not sure of a reference.

   diff, v7, current

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeFeb 16th 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexTo add once editing is back: [abstract clones for abstract syntax](https://arxiv.org/pdf/2105.00969.pdf).

   To add once editing is back: abstract clones for abstract syntax.

5. • CommentRowNumber5.
   • CommentAuthorJ-B Vienney
   • CommentTimeJul 28th 2022
   • (edited Jul 28th 2022)
   • PermaLink
   Author: J-B Vienney
   Format: MarkdownItexIs there any reference on cartesian multicategories or is it brand new research? I would like to use it to conceptualize formal definitions about polynomials between vector spaces as in the chapter 1: Polynomials of the book Complex Analysis on Infinite Dimensional Spaces (Seán Dineen). These things are purely formal and thus cartesian multicategories are maybe the good place to talk about polynomials categorically. I need a place where I can compose a copy map $\Delta^{n}:E \rightarrow E^{n}$ with a $n$-linear map $f:E^{n} \rightarrow F$ and such a composite $\Delta^{n};f$ would be the definition of an homogeneous polynomial of degree $n$ from $E$ to $F$. Maybe such a place would give a cartesian differential category.

   Is there any reference on cartesian multicategories or is it brand new research?

   I would like to use it to conceptualize formal definitions about polynomials between vector spaces as in the chapter 1: Polynomials of the book Complex Analysis on Infinite Dimensional Spaces (Seán Dineen). These things are purely formal and thus cartesian multicategories are maybe the good place to talk about polynomials categorically.

   I need a place where I can compose a copy map $\Delta^{n}:E \rightarrow E^{n}$ with a $n$-linear map $f:E^{n} \rightarrow F$ and such a composite $\Delta^{n};f$ would be the definition of an homogeneous polynomial of degree $n$ from $E$ to $F$.

   Maybe such a place would give a cartesian differential category.

6. • CommentRowNumber6.
   • CommentAuthorvarkor
   • CommentTimeJul 28th 2022
   • (edited Jul 28th 2022)
   • PermaLink
   Author: varkor
   Format: MarkdownItexAdded references. I'm not sure what the earliest reference is, but for now I'm not able to find a reference earlier than Pisani's paper. <a href="https://ncatlab.org/nlab/revision/diff/cartesian+multicategory/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/cartesian+multicategory/8">v8</a>, <a href="https://ncatlab.org/nlab/show/cartesian+multicategory">current</a>

   Added references. I’m not sure what the earliest reference is, but for now I’m not able to find a reference earlier than Pisani’s paper.

   diff, v8, current

7. • CommentRowNumber7.
   • CommentAuthorvarkor
   • CommentTimeMay 17th 2024
   • PermaLink
   Author: varkor
   Format: MarkdownItexAdded the original reference. <a href="https://ncatlab.org/nlab/revision/diff/cartesian+multicategory/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/cartesian+multicategory/12">v12</a>, <a href="https://ncatlab.org/nlab/show/cartesian+multicategory">current</a>

   Added the original reference.

   diff, v12, current