I am struggling to appreciate the definition of locally presentable categories. Can someone please give a naturally occurring example (in geometry or algebra) of a category which is locally presentable (i.e. locally k-presentable for some cardinality k) which is not compactly presentable (i.e. locally finitely presentable)?

For example, according to [Presheaf category is locally finitely presentable](https://math.stackexchange.com/questions/2330795/presheaf-category-is-locally-finitely-presentable) presheaf categories are locally finitely presentable.