1. My approach is "foundational". On the one hand, I am motivated by the problem of the foundations of mathematics (an unsolved problem as far as I am concerned). On the other hand-- and this is more relevant here--, I start "from scratch", and thus what I say can be understood with little technical knowledge. I only assume a modest amount of category theory as background. I will talk informally about technical matters that are written down formally elsewhere, where they can be studied further. [The text in square brackets [-] is either some technical explanation, or a digression.] 2. Terminology First, some terminological conventions. I will use the word "category " in its most general sense: weak ω-category. This is completely inclusive: all sorts of "categories " are categories ow. here are two extensions of the original meaning: "weak", and "omega-dimensional". Weak " signifies an indeterminate notion; there are several different specific versions of weak ategory. It can also be used as a vague notion, when one is merely looking at what one woul
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