Is being homotopic - as a relation between two continuous functions, i.e. morphisms in **Top** - definable by categorical means? Can one detect from the context of dots and arrows, whether two parallel arrows in **Top** are homotopic to each other? Or from another ("higher") categorical point of view?

(If this were the case the relationship between **Top** and its quotient category **hTop** was purely categorical and not grounded on extra-categorical properties.)

slightesthint why this is not a real question? – Hans Stricker Sep 15 '12 at 16:54