# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorDavidRoberts
• CommentTimeMay 25th 2018

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.

• CommentRowNumber2.
• CommentAuthorDavidRoberts
• CommentTimeMay 25th 2018

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 25th 2018

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

• CommentRowNumber4.
• CommentAuthorDavidRoberts
• CommentTimeMay 30th 2018

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.

• CommentRowNumber5.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 30th 2018

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

• CommentRowNumber6.
• CommentAuthorDavidRoberts
• CommentTimeMay 30th 2018
• (edited May 30th 2018)

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”.

• CommentRowNumber7.
• CommentAuthorDavidRoberts
• CommentTimeMay 30th 2018

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