Preservation of filtered colimits and cofiltered limits. #
Typically forgetful functors from algebraic categories preserve filtered colimits
(although not general colimits). See e.g.
Future work #
This could be generalised to allow diagrams in lower universes.
A functor is said to preserve filtered colimits, if it preserves all colimits of shape
J is a filtered category.
A functor is said to preserve cofiltered limits, if it preserves all limits of shape
J is a cofiltered category.