filtered colimits commute with finite limits in Ab

filtered colimits commute with finite limits in Category Ab

using:

1. conservative functor preserving limits and colimits and commuting
2. forgetful functor from Ab to Set as conservative functor
3. right adjoint preserves limits and the forgetful set functor as right adjoint

it remains to show, that \(\mathrm{Forget}\) preserves filtered colimits

• todo

https://math.stackexchange.com/questions/1016618/filtered-colimits-commute-with-forgetful-functors