As many of you know, category theorists are currently doing, among other things, a great job in advertising their modern developments. And I must say, this works for me - in particular, I find myself spending more and more time in [nLab](http://ncatlab.org/nlab/show/HomePage) and the [n-category cafe](http://golem.ph.utexas.edu/category/), fully understanding probably tiny bits of what they say there, and feeling that I really should get a grasp of the great picture at some point. My problem is, as for many students from the "analysis camp", almost total lack of background, except maybe some basic algebraic topology and even more basic algebraic geometry.

So the question is - where should I start in order to understand the ideas they refer to?

* Homotopy theory? This looks like a vast subject, and it's not quite clear for me what aspects of it I should learn. Simplicial methods? Model categories? The latter, for instance, seems pretty abstract and unmotivated until you do some "real" homotopy theory, which looks like a great deal to learn.
* Homological algebra? An even more basic-looking thing, so this might be a good idea to learn it first. Again, to what extent? Is the derived category formalism enough?
* Algebraic geometry - etale cohomology, in particular - at least in order to motivate...
* Topos theory? This is just scary...
* Homotopy type theory? Looks relatively self-contained at first glance, but currently not developed enough to help understanding the "real" stuff. Besides, it drags along logic and type theory as prerequisites, which is even farther away from "the meat"...

Edit: there are related questions [here](https://math.stackexchange.com/questions/301366/what-is-the-minimum-required-background-to-understand-articles-in-the-nlab), [here](https://math.stackexchange.com/questions/65559/mathematics-needed-for-higher-dimensional-category-theory?rq=1) and [here](https://mathoverflow.net/questions/74642/if-i-want-to-study-jacob-luries-books-higher-topoi-theory-derived-ag-what) (see Jacob Lurie's answer, it's really helpful).