Hi Lingyuan! @Riccardo_Zanfa and I have some joint work in progress on similar ideas! Your observation about fibrations with adjoints can be extende...

@matthias-hutzler that's very interesting indeed! How does one demonstrate that Morita equivalence?

Personally, I like the theory of categories, since it is intuitively expressible as a two-sorted theory, but the most straightforward way to present c...

I enjoyed reading this; the application to the universal model was particularly satisfying.

Hi Jan, Sorry for taking a while to see your reply. I've just been reading Z. Janelidze and A. Goswami's self-dual axiomatization, and I'm a little ...

Hi Lingyuan! It's always nice to hear from a new student of topos theory.

1/ to be continued. 2/ If you're committed to employing category theory, it's time to get you thinking more categorically. Here is the first example...

The final link confirms what I thought about you misunderstanding what "universal property" means in category theory. You refer to a particular functo...

Addressing your points in order: You know that the category of Sets (as classically conceived) is a Grothendieck topos, right? What are you using ...

@grothenditque There is no need to relegate ZFC to the meta-theory: a topos comes with internal logic built in, and so rather than going to the elemen...

Dear A C O Simon, It seems to me that you have read widely, and have managed to synthesize many ideas that you have encountered into some kind of sy...