The following special cases are obvious:


1. A Grothendieck topos is concretizable ($F \mapsto \times\_i F(i)$)
2. A well-pointed topos is concretizable ($X \mapsto \rm{Hom}(1, X)$)


I looked at some more different examples and they are all obviously concretizable (but I'm just starting to learn topos theory). Is there an elementary topos from which there is no faitfull functor to the category of sets?



Is any elementary topos a concretizable category?
As Ivan Di Liberti suggests in the comments, according to Lemma 1.2 ([Freyd's paper, *Concretness*](https://doi.org/10.1016/0022-4049(73)90031-5), JPAA 1973) every regular well-powered category with equalizers is concretizable. In particular, every locally small elementary topos is concretizable.


