Jason (jcreed) wrote,
Jason
jcreed

This guy has a super awesome category theory blog. I especially liked this post which observes, as has been known for quite some time (but not to me!) that the functions you know and love from Set are just adjunctions in the bicategory Rel where the 0-cells are sets, the 1-cells are relations, and the 2-cells are inclusions of relations — so that there are only trivial equalities between 2-cells. I didn't believe it until I worked it out; the two 1-cells in the adjunction end up being functional and "cofunctional" (for every output, there is a unique input) relations that are the converse of each other.
Tags: math
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