@MatthewTitsworth This one arxiv.org/abs/0803.3652 and most of the other recommended papers are contained in the references section of the linked paper.

@MatthewTitsworth By chance I met a string of people recently who all knew a bit about Reshetikhin-Turaev invariants and the other things linked to this circle of ideas. I wanted to get an expert's opinion on this, because I was intrigued by these dialogues (my own background is far removed from these fields). Because I favor texts where a theory is presented with some concrete application in mind, I was directed to this book (among a whole slew of other articles to read, which I thankfully all remembered), where also some applications of the abstract theory were covered.

@RobinHouston My first gut reaction was "Yes, that is it!!". Then I went through the Contents and now I I'm only "70%" sure it was this book, since I remember that it should have contained something on knots, but this book does'tn really seem to. But maybe I'm not remembering right.

@JosephO'Rourke It's not this book unfortunately, I already checked it out. But thank you for the effort.

@LSpice Yes, there is, but I can't share it here.

@YemonChoi I know it's been some time, since this question was active, but somehow your remark that thinking groups have points is in some cases bad intuition stuck with me. Since for example geometric group theory is about viewing groups as collections of points, this intuition can't be so bad. Could you give me an example concerning group schemes, where this intuition leads you astray ?

@PaulSiegel Do you know a reference where the Lebesgue integral is expressed in the language of categories ? This sound incredibly interesting (and fearsome!) to me.

@DavidRoberts That seems to me to be a really interesting "sociological" phenomenon in mathematics community. A wild thought: Maybe "algebraic thinker" are typically younger than the analysts and therefore more at ease communicating online ?

[cont] And is there a "deeper reason" - whatever that would be - that analytic aspects can't be described using category theory ? Since this could be used as a foundation I probably should say "can't immediately or intuitively be described using category theory" since as a foundation if we can describe a set categorically we could theoretically describe everything.

Could you please give me a reference to a paper using category theory in cognitive science ? I can't image how this application of category theory could really make anything for a cognitive scientist clearer since (in my naive opinion) it would only add additional terminological baggage for someone who (I would again naively think) doesn't operate with mathematical objects so diverse that a very abstract description, as category theory provides, would help him.