  The Crab Nebula is a bright emitter of non-thermal radiation across the
entire accessible range of wavelengths. The spatial and spectral structures of
the synchrotron nebula are well-resolved from radio to hard X-ray emission. The
un-pulsed emission at GeV to TeV energies is mostly produced via
inverse-Compton scattering of energetic electrons with the synchrotron-emitted
photons. The spatial structure observed at these energies provides insights
into the distribution of electrons and indirectly constrains the so-far unknown
structure of the magnetic field in the nebula. Analyzing the LAT data
accumulated over $\sim$9.1 years with a properly refined model for the Crab
pulsar's spectrum, we determined the 68\% containment radius ($R_{68}$) of the
Crab Nebula to be
$({0.0330\pm0.0025_{stat}}{^{+0.0012}_{-0.0075}}_{sys})^\circ$
(${1.98'\pm0.15'_{stat}}{^{+0.07'}_{-0.45'}}_{sys}$) in the 5--500 GeV band.
The estimated systematic uncertainty is based on two factors: (1) different
analysis methods, morphological models and event types, and (2) the
point-spread-function evaluated with observations of Mkn 421. When comparing
the \emph{Fermi} LAT and H.E.S.S. results on the spatial extension, we find
evidence for an energy-dependent shrinking of the Crab Nebula's $\gamma$-ray
extension ($R_{68}\propto E_\mathrm{IC}^{-\alpha}$ where
$\alpha=0.155\pm0.035_{stat}{-0.037}_{sys}$).
