Common meaning of conjugation

Question

If you look for conjugation in wikipedia, you find around 15 different mathematical meanings for this concept.

Is there something in common to all those meanings?

Answer 1

I think the common property of all of them is that the conjugate of the conjugate is the original element. So in more mathy language, all things called conjugate are a map from a class of objects to itself with the property that the square of the map is the identity.

Edit to include postmortes comment: In general a map from a class of objects to itself that squares to the identity is called an involution. Some very common or natural involutions are called conjugate but I think the distinction here is convention and common usage.

Answer 2

If you take a look at a Latin - 'some other language' dictionary then (in the case of English) you will find always something like this

The common in all the "conjugation" related concepts is that something is related/connected to something else. P. ex. the complex number and its complex conjugate.