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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 ...
Nikio's user avatar
  • 351
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 ...
Sergei Akbarov's user avatar
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, ...
Sergei Akbarov's user avatar
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}_{\...
Ivan Di Liberti's user avatar
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 ...
Sergei Akbarov's user avatar
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 ...
Arrow's user avatar
  • 10.4k