A is for Adjoints, they're important, I hear,
B is for Bicat, where 2-cells cohere.
C is for Colimit, a quotient of sum,
D is for Diagram, chasing them's fun.
E is for Eilenberg, of axiom fame,
F is for Functor? didn't catch her name...
G is for Groupoid, where you can always undo,
H is for Homset, and Homology, too.
I's for Identities, lacking complex antics,
J's for Joyal, who made up some semantics.
K is for Kan, extensions left and right,
L's for Lawvere, his calculus a delight.
M's for MacLane — without him where'd we be?
N's for the Nose, on which things agree.
O is for Operads, algebras of trees,
P is for Pointless, like some topologies.
Q is for Quantales, locales in disguise,
R is for Regular, when kernels coequalize.
S is for Sets, in which most still believe,
T is for Topoi, emerging from sheaves.
U's for Underlying, scrapping useless fluff,
V's for V-category, think "homsets with stuff".
W's for this Week, during which Baez finds,
X's for eXcision, with cycles in mind,
Y's for Yoneda, his lemma beneficial,
Z is for Zero, both final and initial.