The carbon cycle is a crucial part of the Earth's ecosystem, facilitating the circulation of carbon among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere. The correct understanding of this cycle is essential for various environmental science studies.

The two major processes involved in the carbon cycle are:

1. Photosynthesis: This process takes place in the chloroplasts of green plants, algae, and some bacteria. During photosynthesis, these organisms convert carbon dioxide (CO₂) from the atmosphere and water (H₂O) into glucose (C₆H₁₂O₆) and oxygen (O₂) using sunlight as an energy source. This can be represented by the equation:
   6 \text{CO}_{2} + 6 \text{H}_{2}\text{O} + \text{light energy} \rightarrow \text{C}_{6}\text{H}_{12}\text{O}_{6} + 6 \text{O}_{2}

   This process not only removes carbon dioxide from the atmosphere but also provides oxygen necessary for the survival of aerobic organisms.

2. Respiration: This process occurs in all living organisms. During respiration, organic compounds (such as glucose) are broken down into carbon dioxide and water, releasing energy that is used for cellular activities. The equation for respiration is the reverse of photosynthesis:
   \text{C}_{6}\text{H}_{12}\text{O}_{6} + 6 \text{O}_{2} \rightarrow 6 \text{CO}_{2} + 6 \text{H}_{2}\text{O} + \text{energy}

   Respiration returns carbon dioxide to the atmosphere, balancing the carbon removed by photosynthesis.

By examining the options provided:

• Photosynthesis and respiration: These correctly represent the dual processes of the carbon cycle, involving the capture of carbon dioxide and its oxidation back to carbon dioxide.
• Deposition and erosion: These are geological processes and do not directly refer to the carbon cycle.
• Fixation and denitrification: These refer to the nitrogen cycle, involving the conversion of atmospheric nitrogen into usable forms and its subsequent release back to the atmosphere.
• Evaporation and transpiration: These processes are part of the water cycle, not the carbon cycle.

Thus, the correct answer is Photosynthesis and respiration, as they are the primary biological processes involved in the carbon cycle, continuously cycling carbon and maintaining ecological balance.