(Co)homology: A Poem

I was recently (avoiding doing my homology homework by) reading through some old poems by Shel Silverstein, author of The Giving TreeA Light in the Attic, and Falling Up to name a few. Feeling inspired, I continued to procrastinate by writing a little poem of my own - about homology, naturally!

 
 
 
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Homology, homology,
I’ve become rather quite fond of thee.
From $\pi_n$ an oasis,
counting holes in weird spaces,
you’re such a great part of topology!

Homology, homology,
although I only know of three:
simplicial to singular,
the third is called cellular,
they're all just making me so happy.

Homology, homology,
labeling things up to homotopy.
With Mayer and Vietoris,
no van-Kampens on your list,
you've the right smidgen of group theory.

Homology, homology,
“What’s that?” I ask, “What’s this I see?”
Your arrows have changed,
your indices rearranged.
Oh no! You've been hit with duality!

Cohomology, Cohomology,
you’re starting to bewilder me.
Co-this and co-that,
it’s hard to keep co-track.
I think I’d just rather write poetry.