The center of a group consists of all elements which commute with everything. Alternatively, the center of a group is the kernel of the homomorphism that assigns to every element its associated inner automorphism. Which of these descriptions admits a natural generalization? Or is there a more systematic approach?

I will explain an abstract framework of universal algebra that provides a general definition of the center (and much more). I will show how this general approach adapts in concrete classes, such as loops, quandles, and most importantly with respect to the subject of the seminar, inverse semigroups.