A semisimple category is an abelian category in which every object is a finite direct sum of simple objects.

A) Why does one impose the finiteness condition here?

B) If one condsiders infinite direct sums does something go wrong?

C) If B) works with no problems, then is this equivaent to a category where all morphisms split?

A semisimple category is an abelian category in which every object is a finite direct sum of simple objects.

A) Why does one impose the finiteness condition here?

B) If one condsiders infinite direct sums does something go wrong?

C) If B) works with no problems, then is this equivalent to an abelian category where exact sequences split?