Non-invertible symmetries are refined notions of symmetries intensively studied recently. I will show that non-invertible symmetries sometimes lead to a surprising consequence on scattering amplitudes --- a modification of crossing symmetry. I will demonstrate this using example of integrable field theories in 1+1 dimensions although the argument holds more generally; also for non-integrable theories. I will also present the results of S-matrix bootstrap, which constrains the space of physically consistent scattering amplitudes with categorical symmetries.