What is Families of pericyclic reactions?

In an electrocyclic reaction a conjugated polyene closes into a ring by forming a $\sigma$ bond between its termini, or the reverse. In a cycloaddition, two $\pi$ systems join into a ring by forming two $\sigma$ bonds; an $[m + n]$ cycloaddition joins components of $m$ and $n$ atoms (or electrons). In a sigmatropic rearrangement a $\sigma$ bond migrates along a $\pi$ system; in an $[i, j]$ shift the bond moves from atoms 1 and 1 to atoms $i$ and $j$ of the two fragments. A cheletropic reaction makes or breaks two bonds to the same atom, as when sulfur dioxide leaves a sulfolene. In an ene reaction an alkene with an allylic hydrogen adds to a $\pi$ bond, the hydrogen moving with it.