filtered colimits

A category has filtered colimits if it has colimits of diagrams indexed by filtered categories.

exact filtered colimits implies filtered colimits and finitely complete

by definition
cocomplete implies finitely cocomplete and filtered colimits and wide pushouts and connected colimits

[dualized] trivial
finite coproducts and filtered colimits implies coproducts

[dualized] The product $\prod_{i \in I} X_i$ is the filtered limit of the finite partial products $\prod_{i \in E} X_i$ where $E$ ranges over the finite subsets of $I$ .
wide pushouts is equivalent to pushouts and filtered colimits

[dualized] To prove $\Leftarrow$ , a wide pullback can be constructed as a filtered limit of finite pullbacks, and finite pullbacks can be reduced to binary products (the empty-indexed pullback always exists). Conversely, assume that wide pullbacks exist in $\mathcal{C}$ . For every object $A$ then the slice category $\mathcal{C} / A$ has wide pullbacks and a terminal object, hence is complete. Since a filtered limit can be finally reduced to such a slice, we are done.
filtered colimits implies sequential colimits

[dualized] trivial
groupoid implies self-dual and epi-regular and pushouts and filtered colimits and right cancellative and well-copowered

[dualized] easy
self-dual and filtered limits implies filtered colimits

trivial by self-duality
self-dual and filtered colimits implies filtered limits

trivial by self-duality

For these categories the database has no info if they satisfy this property or not.