For me, the Transcendental Deduction aims at proving two things:
Categories or pure concepts of understanding must be applied to the manifold of intuitions, i.e, they are necessary for cognition.
Categories or pure concepts are legitimate insofar as they apply to intuitions.
I am not clear on the second part of the argument, nor can I find any passage directly aiming at the second point.
Also, I also understand that some people associate the second argument to Transcedental Schemata portion of the book. However, to me that section only elucidated how inner-sense/time is a common thread between the heterogeneous faculty of sensibility and understanding. That only proves 'how' the two faculties are linked, not why they should be.
Also, if you think this argument is rather given in Schemata, or ALSO given in schemata (since some papers indicate this as well), please explain that. Some papers also indicate that Schemata is redundant since this problem was solved in B-deduction, hence this question.
To summarise: I understand the argument for intuitions without concepts cannot constitute knowledge but what's the argument for the proposition that concepts without intuitions also cannot claim objective knowledge?