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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeMar 12th 2010
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownTried to clarify the history and the relationship between the different models at [[symmetric monoidal smash product of spectra]].

   Tried to clarify the history and the relationship between the different models at symmetric monoidal smash product of spectra.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 12th 2010
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   Author: Urs
   Format: MarkdownThanks, Mike!

   Thanks, Mike!

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 21st 2016
   • (edited Jan 21st 2016)
   • PermaLink
   Author: Urs
   Format: MarkdownItexJust for the purposes of brushing-up, I have given _[[S-module]]_ its own entry (it used to redirect to _[[symmetric smash product of spectra]]_). Then I have tried to harmonize and brush-up the following system of entries bit more: [[model structure on spectra]], [[symmetric monoidal smash product of spectra]] * [[symmetric spectrum]], [[model structure on symmetric spectra]] * [[orthogonal spectrum]], [[model structure on orthogonal spectra]] * [[S-module]], [[model structure on S-modules]] In paticular I gave all of these entries a more comprehensively informative (I hope) paragraph in their Idea-section. Most of these entries nevertheless are still stubby and deserve to be expanded.

   Just for the purposes of brushing-up, I have given S-module its own entry (it used to redirect to symmetric smash product of spectra). Then I have tried to harmonize and brush-up the following system of entries bit more:

   model structure on spectra, symmetric monoidal smash product of spectra

   • symmetric spectrum, model structure on symmetric spectra

   • orthogonal spectrum, model structure on orthogonal spectra

   • S-module, model structure on S-modules

   In paticular I gave all of these entries a more comprehensively informative (I hope) paragraph in their Idea-section.

   Most of these entries nevertheless are still stubby and deserve to be expanded.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 1st 2016
   • (edited Jun 1st 2016)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have started to type in full and expository details of the unified construction of the symmetric smash product of spectra induced from Day convolution of pre-excisive functors. So far I have a section * _[Topological ends and coends](https://ncatlab.org/nlab/show/symmetric+smash+product+of+spectra#TopologicalEndsAndCoends)_ aiming to give a self-contained setup specialized to the case of enrichment over pointed compactly generated topological spaces. Then a section * _[Monoidal topological categories](https://ncatlab.org/nlab/show/symmetric+smash+product+of+spectra#MonoidalTopologicalCategories)_ with just the usual defs, but making explicit the pointed topological enrichment. Then similarly a section * _[Topological Day convolution](https://ncatlab.org/nlab/show/symmetric+smash+product+of+spectra#TopologicalDayConvolution)_ This needs to be expanded. In particular a proof of the [[co-Yoneda lemma]] should be added, and the construction of the internal homs with respect to Day convolution (whence mapping spectra). In the process I also touched _[[Day convolution]]_ itself and tried to harmonize notation throughout. The in the end there is so far just a stub statement about the smash product of pre-excisive functors.

   I have started to type in full and expository details of the unified construction of the symmetric smash product of spectra induced from Day convolution of pre-excisive functors.

   So far I have a section

   • Topological ends and coends

   aiming to give a self-contained setup specialized to the case of enrichment over pointed compactly generated topological spaces.

   Then a section

   • Monoidal topological categories

   with just the usual defs, but making explicit the pointed topological enrichment.

   Then similarly a section

   • Topological Day convolution

   This needs to be expanded. In particular a proof of the co-Yoneda lemma should be added, and the construction of the internal homs with respect to Day convolution (whence mapping spectra).

   In the process I also touched Day convolution itself and tried to harmonize notation throughout.

   The in the end there is so far just a stub statement about the smash product of pre-excisive functors.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJun 2nd 2016
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have now added an elementary point-set topology derivation of the co-Yoneda lemma for enrichment in pointed topological spaces [here](https://ncatlab.org/nlab/show/symmetric+smash+product+of+spectra#TopologicalCoYonedaLemma).

   I have now added an elementary point-set topology derivation of the co-Yoneda lemma for enrichment in pointed topological spaces here.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJun 10th 2016
   • (edited Jun 10th 2016)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have brought in all the remaining infrastructure into the entry. Then I wrote out a derivation, from first principles (via Day convolution), of the symmetric monoidal smash product of symmetric (and orthogonal) spectra -- [here](https://ncatlab.org/nlab/show/symmetric+smash+product+of+spectra#ForSymmetricAndOrthogonalSpectra).

   I have brought in all the remaining infrastructure into the entry. Then I wrote out a derivation, from first principles (via Day convolution), of the symmetric monoidal smash product of symmetric (and orthogonal) spectra – here.