Visual mnemonics for Category Theory

Visual mnemonics for Category Theory

[Brian Ledger]

Dana Scott said the other day, in a presentation, "Haskell Curry was the
only Mathematician I ever knew who could see a concept only in terms of
symbols." I think that's a rather elegant compliment to Curry, and
conversely, I think it says a lot about how we think about Mathematics,
since we are not all Haskell Curry.

I'm venturing that a lot of us expose our ideas systematically, but, in the
back end, we have our own devices, which let us understand difficult
concepts, and render new insight through their manipulation.

I'm curious what sort of devices we have.

I know that some purists are probably shifting uneasily at this.

However, I wonder why we call the application of a functor a "lifting", and
why a fibration F: E -> C suggests that "E lies over C", and we are all
very happy to draw a little loop over an object to denote a fiber. This
comes from somewhere.

Why do we call epis and monos "split" if they have an inverse? Why is the
pseudo-inverse of a fibration called a "cleavage"? I literally picture a
bundle of fibers getting cleaved by an axe-like object in my mind's eye.


I'm actually fairly new to Category Theory, and I'm wary of mental models
that would take me down the wrong path, or deprive me of the elegance of a
fully symbolic understanding. However, I don't aspire to be great at
Mathematics. I'm just not that good. It would be wonderful if I could share
in some mental helpers that would give me insight into the topics I'm
studying.

- Brian


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