# Is homotopy definable by categorical means?

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.)

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This is close to a question of Daniel Miller: mathoverflow.net/questions/92206 –  Tom Leinster Sep 15 '12 at 16:06
@twimc: could you please give me the slightest hint why this is not a real question? –  Hans Stricker Sep 15 '12 at 16:54
@HansStricker Have you take a look to this: ncatlab.org/nlab/show/homotopy . –  Giorgio Mossa Sep 15 '12 at 17:07
Thanks to Tom and Giorgio: that gives me to study a lot! –  Hans Stricker Sep 15 '12 at 17:56
you're welcome :) –  Giorgio Mossa Sep 15 '12 at 20:47