I don't have very good intuition for split epis/monos
suppose i have a fiber bundle E->B
a splitting of this is a global section, so it's a split epi iff it *admits a global section*. This seems like... kind of a weird thing to be *such* a fundamental categorical concept
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i guess i have two intuitions here; one is that split epis/monos are equational and so preserved by arbitrary functors (which characterizes them), and the other is about splitting idempotents
split epis and monos are sort of the closest you can get 1-categorically to adjoint functors. the two stories are surprisingly parallel. the idempotent corresponds to the monad / comonad and so forth
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oh i like this one!
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