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Apr 30, 2017 at 19:55 comment added Ingo Blechschmidt $\mathbf{Set}^\mathrm{op}$ is equivalent to the category of complete atomic Heyting algebras (you may read "complete atomic Boolean algebras" here, if you're willing to work in classical logic) and therefore concrete as a subcategory of a concrete category.
Dec 13, 2014 at 6:13 comment added Zhen Lin In fact, $\mathbf{Set}^\mathrm{op}$ and $\mathbf{Rel}$ are concrete. First, note that the former embeds in the latter in an obvious way. Then note that $\mathbf{Rel}$ can be embedded in $\mathbf{Set}$ by sending each set $X$ to $2^X$.
Dec 13, 2014 at 0:52 history answered Anton Fetisov CC BY-SA 3.0