CREATE TABLE table_22369 ("Institution" TEXT, "Location" TEXT, "Founded" FLOAT, "Years in IIAC  ( approx. ) " TEXT, "Team Nickname" TEXT)

List all institutions with a team name of the Cardinals.
SELECT "Institution" FROM table_22369 WHERE "Team Nickname" = 'Cardinals'
SELECT "Institution" FROM "table_22369" WHERE "Team Nickname" = 'Cardinals'