Zhant

There is a functor [; ({-})^{\ast} ;] from the category of hosts [; \textsf{Host} ;] to its dual category of cohosts [; \textsf{Cohost} \equiv \textsf{Host}^{\text{op}} ;] which sends every host [; H ;] to its cohost [; H^{\ast} ;] and every morphism between hosts (i.e., every post) [; f \colon H \rightarrow J ;] to the dual chost [; f^{\ast} \colon J^{\ast} \rightarrow H^{\ast} ;] given by [; f^{\ast}(j^{\ast}) = j^{\ast}(f({-})) ;].

It is self-adjoint, when viewed as a contravariant endofunctor of [; \textsf{Host} ;], but this joke is already past its funniness and its completion is left as an exercise for the reader.

(native MathJax support would be cool ngl)

Also if I had the css skills and/or time I would have hardcoded the LaTeX myself and changed the usual asterisk to a little eggbug but my bachelor's thesis is due in like two weeks and I shouldn't procrastinate too much