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I am trying to understand the concept of locally finitely presentable categories. I have discovered the concept of compact object here. I have discovered that for groups, the finitely presented groups are precisely the compact objects in Grp (the category of groups). I have also discovered that Grp is locally finitely presentable. This means that Grp contains objects that are not compact. Compact objects are also referred to as finitely presentable objects. I am assuming that I am confusing the terminology. Basically, how can Grp be locally finitely presentable, if it contains objects that are not finitely presentable?

Here is a link that states the Grp is locally finitely presentable. It is stated in example 4.

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"Locally finitely presentable" does not imply that every object is finitely presentable. What it implies is that every object is the filtered colimit of finitely presentable objects, which is true of $\text{Grp}$.

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