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1. • CommentRowNumber1.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 25th 2018
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexThe inductive tensor product is the analogue of the projective tensor product where we have a universal property wrt separately continuous maps. For Fréchet spaces they agree. <a href="https://ncatlab.org/nlab/revision/inductive+tensor+product/1">v1</a>, <a href="https://ncatlab.org/nlab/show/inductive+tensor+product">current</a>

   The inductive tensor product is the analogue of the projective tensor product where we have a universal property wrt separately continuous maps. For Fréchet spaces they agree.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 25th 2018
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAdded floating toc and contents. <a href="https://ncatlab.org/nlab/revision/inductive+tensor+product/1">v1</a>, <a href="https://ncatlab.org/nlab/show/inductive+tensor+product">current</a>

   Added floating toc and contents.

   v1, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 25th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a bunch of hyperlinks to various technical terms in the first few paragraphs. in particular I made sure that there are links back to _[[tensor product]]_ and _[[tensor product of vector spaces]]_. Conversely, I made these entries also point to _[[inductive tensor product]]_ <a href="https://ncatlab.org/nlab/revision/diff/inductive+tensor+product/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/inductive+tensor+product/2">v2</a>, <a href="https://ncatlab.org/nlab/show/inductive+tensor+product">current</a>

   added a bunch of hyperlinks to various technical terms in the first few paragraphs. in particular I made sure that there are links back to tensor product and tensor product of vector spaces. Conversely, I made these entries also point to inductive tensor product

   diff, v2, current

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 30th 2018
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAdded original reference to Grothendieck's nuclear spaces monograph, added theorem about further properties: the tensor product commutes with inductive limits and makes $lctvs$ a symmetric monoidal closed category. <a href="https://ncatlab.org/nlab/revision/diff/inductive+tensor+product/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/inductive+tensor+product/3">v3</a>, <a href="https://ncatlab.org/nlab/show/inductive+tensor+product">current</a>

   Added original reference to Grothendieck’s nuclear spaces monograph, added theorem about further properties: the tensor product commutes with inductive limits and makes $lctvs$ a symmetric monoidal closed category.

   diff, v3, current

5. • CommentRowNumber5.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMay 30th 2018
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexIs this result about lctvs as a closed symmetric monoidal category due to Grothendieck?

   Is this result about lctvs as a closed symmetric monoidal category due to Grothendieck?

6. • CommentRowNumber6.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 30th 2018
   • (edited May 30th 2018)
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexNot sure. I saw it in Ralf Meyer's book on cyclic homology, but it was a throwaway comment, together with the complaint that it's not very useful, due to the problem with the completed inductive tensor. Sydow, in _[On hom-functors and tensor products of topological vector spaces](https://doi.org/10.1007/BFb0066910)_, dating from 1982, says "it is is easy to see".

   Not sure. I saw it in Ralf Meyer’s book on cyclic homology, but it was a throwaway comment, together with the complaint that it’s not very useful, due to the problem with the completed inductive tensor.

   Sydow, in On hom-functors and tensor products of topological vector spaces, dating from 1982, says “it is is easy to see”.

7. • CommentRowNumber7.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 30th 2018
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAndrew Stacey talks through the issue in [this comment](https://golem.ph.utexas.edu/category/2008/01/comparative_smootheology.html#c015601) (and following) from ten or so years ago. He refers to [this book](https://doi.org/10.1007/978-1-4612-1468-7) for details.

   Andrew Stacey talks through the issue in this comment (and following) from ten or so years ago. He refers to this book for details.