I'm not actually a category theorist, but assume I have some background in category theory and am pretty comfortable with it; and I want to learn higher category theory (say in the sense of Boardmann-Vogt-Joyal-Lurie) but don't want to have to delve into the intricacies of simplicial sets and anodyne extensions and other scary-looking things (to the eyes of someone who isn't very good in combinatorics and dealing with indices)
I've read in several places (but there was just a sentence or 2) that it would be possible to actually just learn "the language" of $(\infty,1)$-categories, how they are manipulated etc. without having to go through said intricacies.
A comment by Qiaochu Yuan on another post had the same idea, but explicitly stated that he didn't know where to find such a treatment. The passage that mainly sums up what I'm looking for is :
" learn some model-independent things that ought to be true in all models of (∞,1)-categories (e.g. formal statements about the behavior of homotopy limits and colimits)"
I would add "behavior of functor categories, adjoints, (Kan extensions if they make sense ?)" and other nifty $1$-categorical stuff, done homotopically. Emily Riehl's model-independent approach has been mentioned a bunch of times, but when I tried to see what it was about (the title sounded promising) I realized that it relied (I don't know how heavily, but at least it required some stuff) on the already existing theory of $\infty$-categories, which I would therefore have to learn (with the afore-mentioned intricacies) before learning this model-independent treatment, which would defeat (some of) the purpose of learning the model-independent story (I guess a subquestion would be : how much of "model-dependent" $\infty$-category theory does one have to go through before reading Riehl's approach ?)
Is there such a treatment ?
To be more precise, I would be fine with a document that says stuff like "this works well because we can check it simplicially" and then moves on to build on these "simplicial stones hidden under the rug" and actually do some proofs that are more "categorical" in a sense, based on these accepted principles.