filtered colimits commute with finite limits in RMod
1. Proposition
Given category RMod, filtered colimits commute with finite limits
2. Proof
corollary of:
- filtered colimits commute with finite limits in Ab
- forgetful functor from RMod to Ab as right adjoint / forgetful functor from RMod to Ab as left adjoint
- right adjoint preserves limits / left adjoint preserves colimits
- forgetful functor from RMod to Ab as conservative functor
- conservative functor preserving limits and colimits and commuting
- conservative right adjoint creates limits for a sufficiently complete domain