The catalyst in photosynthesis is:

The work of chlorophyll is to absorb light energy from sunlight and transfer it to other molecules used for a process of photosynthesis. This energy is utilized in synthesize carbohydrates using $C{O}_2$.

Further, it also doesn't use in a reaction of photosynthesis hence it acts as the catalyst in this reaction.
Complete balanced chemical equation is $6H_{2}O+6C{O}_2\to C_6{H}_{12}{O}_6+6O_2$