# 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.
• CommentAuthorDavid_Corfield
• CommentTimeJul 5th 2018

Had a look at some literature and found of course that it’s vast, so have added some findings.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJul 5th 2018

(It’s so easy to include keywords in double brackets!, and so very useful for the reader!, especially for newbies to the topic. I suggest making it a habit.)

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeJul 5th 2018

I’m wondering now how consistent is the naming in this neck of the words, especially transporter category and Frobenius category. The latter does not mean Frobenius category. We’re coming close here to the intricate world of fusion systems.

I’ve left a reference where I took the terminology from.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeApr 14th 2021

Have moved discussion of Properties out of the Definition-section.

Have replaced the tom Dieck-reference item with a hyperlinked version:

(which means I had to remove the experimental bibtex functionality, for the time being)

and I changed the wording around that reference:

The term “EI-category” is not actually in that book, is it? What is there, on p. 73, is the explicit observation that “endomorphisms are automorphisms” on the orbit category and its relatives.

So I have made the wording refer to that verbiage on that page now, instead. But let me know if I am missing something.

• CommentRowNumber5.
• CommentAuthorvarkor
• CommentTimeMay 10th 2021
• (edited May 10th 2021)

Does anyone have any nicer names for this concept? I find “EI” to be a confusing term, because “I” could stand for either “isomorphism” or “identity” (the latter being the defining property of one-way categories). An actual adjective would be more aesthetic as well.

• CommentRowNumber6.
• CommentAuthorMike Shulman
• CommentTimeMay 10th 2021

It’s a pretty standard term, unfortunately. (Perhaps you meant to refer to gaunt categories for the other notion; they don’t have to be direct.)

• CommentRowNumber7.
• CommentAuthorvarkor
• CommentTimeMay 11th 2021

Perhaps you meant to refer to gaunt categories for the other notion; they don’t have to be direct.

Oh, the nLab entry for one-way categories is a little misleading at the moment, because they’re defined on the page for direct categories; however, one-way categories do not have to be direct. Perhaps it would be better to give them their own page.

• CommentRowNumber8.
• CommentAuthorMike Shulman
• CommentTimeMay 11th 2021

Yes, I realized actually gaunt is somewhat different, that means every isomorphism is an identity, but you mean every endomorphism is an identity.

I don’t think I’ve ever heard anyone talk about one-way categories that aren’t direct, but I guess the definition allows that. The terminology seems somewhat strange in that case, though; what’s “one-way” about a category with this sort that isn’t direct? In particular, it doesn’t have to be skeletal, does it?

• CommentRowNumber9.
• CommentAuthorvarkor
• CommentTimeMay 11th 2021

The terminology seems somewhat strange in that case, though; what’s “one-way” about a category with this sort that isn’t direct? In particular, it doesn’t have to be skeletal, does it?

I agree: “one-way” doesn’t seem like an accurate description unless you also impose that the category is skeletal (in which case you have an acyclic category).

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeDec 27th 2021

added (here) pointer to one more example: tom Dieck’s fundamental category of a $G$-space

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeDec 27th 2021

added a couple more references on representation theory of EI-categories, and gave the list of references a little more structure