There can be positive and negative catalysts, according to the catalyst’s effect on the rate of reaction. The key difference between positive and negative catalysts is that positive catalysts are substances that are capable of increasing the reaction rate, whereas negative catalysts are substances that are capable of decreasing the reaction rate. A positive catalyst works by lowering the activation energy to speed up the reaction; however, a negative catalyst cannot lower the activation energy, so the reaction rate is decreased.
Noor Aljammal, The relationship between the activation energy and the rate of a chemical reaction is not always as you write, i.e. increase-decrease or decrease-increase. The rate of a chemical reaction depends on the catalyst used, as well as on the reactants, the concentration of substrates, temperature, and in the case of gas-phase reactions, also on pressure. Furthermore, in the case of "negative catalysts" we usually use the term inhibitor, although this term may have a wider meaning.
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