The Category of Vector Spaces: Quotient Vector Spaces (Lecture 6)

Among the most important constructions in set theory is the notion of a quotient set, which promotes an equivalence relation to actual equality. Naturally, we would like to understand when a quotient of a vector space is canonically a vector space, and we are thus led to the notion of a quotient vector space. This notion is very tightly related to the notion of subspace.