There's one for every cardinality (up to isomorphism). I forget my set theory, but if the cardinalities form a set, then the totality of vector spaces does too.

There's one for every cardinality (up to isomorphism). I forget my set theory, but if the cardinalities form a set, then the totality of vector spaces does too. If not, we can amuse ourselves by looking at the set of finite-dimensional vector spaces.