# Some results on locally finitely presentable categories

@article{Makkai1987SomeRO, title={Some results on locally finitely presentable categories}, author={Michael Makkai and Andrew M. Pitts}, journal={Transactions of the American Mathematical Society}, year={1987}, volume={299}, pages={473-496} }

We prove that any full subcategory of a locally finitely presentable (l.f.p.) category having small limits and filtered colimits preserved by the inclusion functor is itself l.f.p. Here "full" may be weakened to "full with respect to isomorphisms." Further, we characterize those left exact functors I: C -+ D between small categories with finite limits for which the functor I*: LEX(D, Set) -+ LEX(C, Set) induced by composition is full and faithful. As an application, we prove a theorem on sheaf…

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