  In the present paper, we use the holographic approach to describe the
early-time acceleration and the late-time acceleration eras of our Universe in
a unified manner. Such ``holographic unification'' is found to have a
correspondence with various higher curvature cosmological models with or
without matter fields. The corresponding holographic cut-offs are determined in
terms of the particle horizon and its derivatives, or the future horizon and
its derivatives. As a result, the holographic energy density we propose is able
to merge various cosmological epochs of the Universe from a holographic point
of view. We find the holographic correspondence of several $F(R)$ gravity
models, including axion-$F(R)$ gravity models, of several Gauss-Bonnet $F(G)$
models and finally of $F(T)$ models, and in each case we demonstrate that it is
possible to describe in a unified way inflation and late-time acceleration in
the context of the same holographic model.
