  Quandle homology was defined from rack homology as the quotient by a
subcomplex corresponding to the idempotency, for invariance under the type I
Reidemeister move. Similar subcomplexes have been considered for various
identities of racks and moves on diagrams. We observe common aspects of these
identities and subcomplexes; a quandle identity gives rise to a $2$-cycle, the
abelian extension with a $2$-cocycle that vanishes on the $2$-cycle inherits
the identity, and a subcomplex is constructed from the identity. Specific
identities are examined among small connected quandles.
