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ABSTRACT Spider pulsars are binary systems composed of a millisecond pulsar and a low-mass companion. Their X-ray emission, varying with orbital phase, originates from synchrotron radiation produced by high-energy electrons accelerated at the intrabinary shock. For fast-spinning pulsars in compact binary systems, the intrabinary shock emission occurs in the fast cooling regime. Using global 2D particle-in-cell simulations, we investigate the effect of synchrotron losses on the shock structure and the resulting emission, assuming that the pulsar wind is stronger than the companion wind (so, the shock wraps around the companion), as expected in black widows. We find that the shock opening angle gets narrower for greater losses; the light curve shows a more prominent double-peaked signature (with two peaks just before and after the pulsar eclipse) for stronger cooling; below the cooling frequency, the synchrotron spectrum displays a hard power-law range, consistent with X-ray observations.