According to Wikipedia:
Chemical reactions occur faster in the presence of a catalyst because the catalyst provides an alternative reaction pathway with a lower activation energy than the non-catalyzed mechanism. In catalyzed mechanisms, the catalyst usually reacts to form a temporary intermediate, which then regenerates the original catalyst in a cyclic process.
Since catalysts react in intermediate reaction and hence in the rate-determining step, is it possible that they appear in the kinetic rate equation?
If so are there some examples?
Edit: For more clarity I encountered this doubt in a true or false question which went like this:" Catalyst can appear in kinetic rate equation".
Edit 2: As told in the comments, another similar question says specifically that catalyst are not included in rate equations, but the question I encountered says it might sometimes. So there is some irregularity in my question which seems highly unlucky to me as I have read some examples like hydrolysis of esters where rate is directly proportional to H+ concentration.
Am I wrong?