Notes for February 5, 2018

What I learned today:

Functors have to preserve both objects and morphisms

In most common categories (locally small ones), the hom-sets are, well, sets.

Read Sutton 16.1 and 16.2.

Termination functions generalize discounting, and make more intuitive sense. Discounting always felt like a hack to me, since they mostly seem to exist to make sums converge.

The Kleene star is just the free monoid construction. I’ve started using the star and plus operators in type signatures since they’re really handy for functions of arbitrarily many arguments.

Thought about the coarseness and fineness of equivalence relations.

For my money, memorizing the definition of equivalence relations and their equivalence to partitions of a set is one of the biggest no-brainers.

Category theory has a lot of terminology.

Alberto Rodriguez gave a talk that included the phrase “ladder of shame”. Stealing that.

It’s funny that vim’s spell checker is the best one I’ve used simply because it doesn’t give dodgy autocorrect and if mapped to automatically use the first suggestion, is really fast. I can check a page in about 15 seconds. It’s also the only reason this note has proper capitalization.

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Way to remember the definition of local finiteness