once upon a time, in the land of mathlandia, the people in the city of algebraic geometria had a brilliant vision: what if all math was algebra, every theorem was category theory, and every proof used cohomology? armed with their categories and rings, they declared war on the other cities of mathlandia. number theoryberg was the first to fall, succumbing to the glory of sheaves and schemes. next was representation theory city, which fell soon after. but alas, despite their efforts the algebraists had not made any progress since... until now! scholze and clausen have started the condensed mathematics program, which vows to take over functional analysisberg and differential geometria. we will deal with the very first matter in this program, the story of locally compact abelian groups.