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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 4th 2016
   • PermaLink
   Author: Urs
   Format: MarkdownItexCreated a stub entry for _[[norm map]]_, for the moment just so as to make cross-links work.

   Created a stub entry for norm map, for the moment just so as to make cross-links work.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 4th 2025
   • (edited May 4th 2025)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Michael Hopkins]], [[Jacob Lurie]]: Remark 4.1.12 of: *[[Ambidexterity in K(n)-Local Stable Homotopy Theory]]* (2014) <a href="https://ncatlab.org/nlab/revision/diff/norm+map/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/norm+map/5">v5</a>, <a href="https://ncatlab.org/nlab/show/norm+map">current</a>

   added pointer to:

   • Michael Hopkins, Jacob Lurie: Remark 4.1.12 of: Ambidexterity in K(n)-Local Stable Homotopy Theory (2014)

   diff, v5, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 4th 2025
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIs this the same 'norm map' as the one corresponding to multiplicative transfer discussed at [[Tambara functor]]?

   Is this the same ’norm map’ as the one corresponding to multiplicative transfer discussed at Tambara functor?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 4th 2025
   • (edited May 4th 2025)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe same type of map: going from a left adjoint $f_!$ to a right adjoint $f_*$, such that it is an equivalence when the adjoint triple $f_! \dashv f^\ast \dashv f_\ast$ is ambidextrous.

   The same type of map: going from a left adjoint to a right adjoint , such that it is an equivalence when the adjoint triple is ambidextrous.

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 5th 2025
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexHmm. I thought the 'N' for norm of 'TNR' was the middle map in that passage along a polynomial, the multiplicative part. > norms given by tensor-induction > \[ N_K^H(V)_x \simeq \bigotimes_{q(y) = x} V_y. > \] and > The **Burnside Tambara functor** has coefficient system $\mathcal{A}(-)$, transfers given by induction, and norms given by coinduction Rather than a comparison map, the coinduction map itself.

   Hmm. I thought the ’N’ for norm of ’TNR’ was the middle map in that passage along a polynomial, the multiplicative part.

   norms given by tensor-induction

   and

   The Burnside Tambara functor has coefficient system , transfers given by induction, and norms given by coinduction

   Rather than a comparison map, the coinduction map itself.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMay 5th 2025
   • PermaLink
   Author: Urs
   Format: MarkdownItexI think they say "Norm" for the wrong-way map (Umkehr map) which is induced by the actual norm map (cf. eg. [here](https://mathoverflow.net/a/209867/381), for a quick link). But I admit that I don't have the leisure to sort out what they write, and if I am wrong and they are using "Norm" in an unrelated way, then somebody please correct me.

   I think they say “Norm” for the wrong-way map (Umkehr map) which is induced by the actual norm map (cf. eg. here, for a quick link).

   But I admit that I don’t have the leisure to sort out what they write, and if I am wrong and they are using “Norm” in an unrelated way, then somebody please correct me.