An object in this meaning is the same thing as an objective[?] or task[?]. It comes from old project terminology and refers to the act of actually performing something according to a plan, or rather "according to a project" (the word "project" used to mean "plan").
... the doctrines of Hegel and Schleiermacher. After holding the chair of philosophy at Halle for two years, he became, in 1833, professor at the university of Königsberg[?], ...