@DenisNardin doing it model-independent and pay the price that some foundations has to be taken for granted is an option? if not what about saying once what is a q.c. and then work completely model-independent without proving any of the basic features? this is more or less what we had in the SAG seminar in the Hebrew university and it was really fun in my opinion, especially for courses which are not specifically on infinity categories.
@S.carmeli I'm happy to do that, but how do you give examples? (I am a strong believer in giving examples)
Or rather, how do you explain what an ∞-category is?
I'd expect a master student to have had at best an introduction to homotopy theory where they learned the Serre spectral sequence and basic properties of the higher homotopy groups. I don't know how much that is a faithful description of reality, but I know that my own master education did not even go that far until the last semester
@DenisNardin I can send you the notes I typed back then, maybe it will be of some help, even though it was simultaneous typing and its not exactly what was on the board. Of course, im not sure that this is the best approach and we had not many examples actually (we sort of seen how you get from spaces to spectra with their symmetric monoidal structure quite quikly from the basic axioms though which was cool)
@DenisNardin Regarding introduction infty-categories, at the Hebrew university we also had a Kan seminar, aimed at master&phd students, where some of the results were presented infty-categorically and used spectra.
Therefore, I gave an introductory (2h) talk on infty-categories and spectra, and I think it went well, even for the people who heard about it for the first time.
The talk was model-independent, and gave some examples for "explicit" things, and relationships to things people already know.
