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## Discussion Tag Cloud

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

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeOct 31st 2013

added to orbit category a remark on what the name refers to (since I saw sonebody wondering about that)

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeOct 31st 2013

Since Mackey functor is only a stub, I added a ’Guide’ in the references

• CommentRowNumber3.
• CommentAuthorDavidRoberts
• CommentTimeNov 1st 2013

Some small changes at orbit category (including making $\mathrm{Or}\, G$ into $\operatorname{Or}G$ throughout).

• CommentRowNumber4.
• CommentAuthorTodd_Trimble
• CommentTimeNov 1st 2013
• (edited Nov 1st 2013)

The difference between the results of \mathrm{}\backslash, and \operatorname{} is invisible to my eyes.

• CommentRowNumber5.
• CommentAuthorDavidRoberts
• CommentTimeNov 1st 2013
• (edited Nov 4th 2013)

The space induced by the backslash-comma combination looked too big to me. But never mind.

• CommentRowNumber6.
• CommentAuthoradeelkh
• CommentTimeNov 4th 2013
• (edited Nov 4th 2013)

There is also another construction which goes by the name of “orbit category”: when $T : \mathcal{A} \to \mathcal{A}$ is an additive automorphism, the orbit category $\mathcal{A}/T$ is the one with the same objects as $\mathcal{A}$, and in which morphisms are given by $\mathcal{A}/T(X, Y) = \bigoplus_{i \in \mathbf{Z}} \mathcal{A}(X, T^i(Y))$. This has appeared under the name “orbit category” in papers of Keller, Tabuada, and others. Perhaps we should mention this somewhere on the page?

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeNov 4th 2013

If you have time, please do!

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeOct 24th 2020
• (edited Oct 24th 2020)

added graphics showing the orbit categories of the first five cyclic groups (here)

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMar 17th 2021

added pointer to the original:

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMar 17th 2021

added pointer to:

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeMar 17th 2021

maded more explicit that and where Dwyer-Kan gave the general definition:

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTime6 days ago

added the remark (here) that, at least for discrete groups, the category of $G$-sets is the free coproduct completion of the orbit category.

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