Horrible answers to "What is a type?"

A set. Absolutely not a set. An element of a category. A proposition. A chosen fixed point of a generating function. The initial algebra&#x2F;final coalgebra of a generating endofunctor over a reasonable base category (say, Set ). A metaphorical representation of bytes. A membership function UNIV → bool . That thing you put after the : to make the computer stop yelling at you :( as any Propaganda…