Well, to be fair, Bartosz does make a lot of references to those things and without a certain background you will have to google them

To be honest, i do not remember very good Bartosz book ;-)

can you please recall some example of this?

I have near to nothing experience regarding mentioned areas, still hadn't any issues reading Bartosz's blog.

I think Bartosz used terms like "sets" and "classes" right where he was explaining the notion of small categories. It's not really complicated, but still is a valid example of what I was referring to

Well, you don't need to know ZFC set theory properly to understand those things

I think I'll agree there. I guess what I'm trying to say is that you don't need deep knowledge of those areas, but basic knowledge would help a lot

NBG set theory ;-)

I suppose wikipedia level will suffice

I agree. The question was what is useful in regards to TC. Thats what is useful. The mathematical analysis or mathematical physics is not useful for example, as they deal with concretics rather than abstractions.

There are people who might disagree

You can study TC without any math. Even though other math areas may be useful to understand how proof works in math. Also they might be easier to grasp as they are more concrete.

If Alice reads Milewski, she is probably a coder and would be pleased to find haskell examples, if Bob is a physicist, physics examples would be more useful for him, both are likely to have same amount of cathegory theory knowledge

So it would be useful to have some profession and some book  using examples from the related domain

FYI Они в МИТе курс по этой книжке в разных вариациях читают.

I did read Bartosz. Finished but I feel like I lack of basic math knowledge.

And currently I also watch his videos in youtube. Not finished yet. Still chapter II.

The thing is I have to read the book many times. And also watch with many replay.

BTW, t.me/appliedcategorytheory

Такое вот.
Products and coequalizers in pointed categories
Michael Hoefnagel
https://arxiv.org/abs/1910.12517
Из "main results" —
If C is a pointed category with binary products which satisfies (P), then the product of two normal epimorphisms is normal, and in particular C has normal projections.
#paper

You should try to take notes and drawings on paper while reading or watching. It really helps. TC is deeply hardwiered in the motion centers of brain, as Milewsky points.

Не подскажете ли, где можно почитать философские (ну, качественные) объяснения того, что такое экспоненциал? Я вот чего не понимаю.

Возьмём категорию Hask. Объекты — это типы, типизированные термы - это морфизмы. Но что тогда такое lambda? Отображение, переводящее терм в форме lambda (x, y) ... в терм в форме lambda x. lambda y ... и "сохранение" его во множестве a -> b -> c? То есть, чисто текстовое такое преобразование? Но это как-то расходится с тем, что про lambda пишут в большинстве других случаев, где lambda — это нечто вроде конструктора кода вычисления.

Что бы такое почитать, чтобы прояснить все детали? С абстрактной точки зрения, конечно, определение очевидно. Но вот концептуально я плыву.