All Questions
6
questions
8
votes
1
answer
421
views
Why are enriched (co)ends defined like that?
I'm mainly following references such as Kelly, Loregian and the nLab, and it seems customary there to generalize (co)ends to the enriched context (over a symmetric monoidal category $\mathcal{V}$) by ...
6
votes
0
answers
856
views
Tannaka without Yoneda?
I am studying enriched categories, and as I wrote in my previous question How is the morphism of composition in the enriched category of modules constructed?, this is very difficult because there are ...
5
votes
2
answers
580
views
How is the morphism of composition in the enriched category of modules constructed?
I asked this a week ago at MSE, but without success.
I am studying enriched categories and I have a feeling that I am doing something wrong because all the way each step, each elementary proposition, ...
3
votes
2
answers
337
views
The symmetric monoidal closed structure on the category of $\mathcal{F}$-cocomplete categories and $\mathcal{F}$-cocontinuous functors
In 6.5 of the book by Kelly,
Basic concepts of enriched category theory. Reprints in Theory and Applications of Categories, No. 10, 2005.
the author claims that the $2$-category $\mathsf{Cat}_{\...
5
votes
1
answer
340
views
Tannaka duality for closed monoidal categories
I asked this some time ago at mathstackexchange, and people there explained to me the mathematical part of what I was asking, but the question about references remains open. In my impression, people ...
13
votes
2
answers
1k
views
The category of elements, enrichment, and weighted limits
This is a crosspost of this MSE question.
Every so often, when reading notes online or skimming through books, the category of elements and the Grothendieck construction pop up. I don't know anything ...