Determine the hybridization orbitals for C & N in C2N2?

For sp, sp² and sp³ hybridization, the hybridized orbitals are used to make σ bonds and lone pairs, while the unhybridized p orbitals are used to make π bonds.

The structure of C₂N₂ is :N≡C-C≡N:

In C₂N₂, the C atom is sp hybridized.
Each C atom has 1 triple bond (i.e. 1 σ bond and 2 π bonds) and 1 single bond (i.e 1 σ). In other words, each C atom has 2 σ bonds and 2 π bond. There would be 2 hybridized orbitals to form the 2 σ bonds, and 2 unhybridized p orbitals to form the 2 π bonds. Therefore, the C atom is sp hybridized. Besides, the linear shape also shows that the C atom is sp hybridized.

In C₂N₂, the N atom is also sp hybridized.
Each N atom has 1 triple bond (i.e. 1 σ bond and 2 π bonds) and 1 lone pair of electrons. In other words, each C atom has 1 σ bond, 2 π bonds and 1 lone pair of electrons. There would be 2 hybridized orbitals to form the σ bond and the lone pair of electrons, and 2 unhybridized p orbitals to form the 2 π bonds. Therefore, the C atom is sp hybridized. Besides, the line shape of the triple bond and lone pair also shows that the N atom is sp hybridized.