What process allows a cell to take in material through infolding of the cell membrane?

The process that allows a cell to take in material through infolding of the cell membrane is known as endocytosis. During endocytosis, the cell membrane forms a pocket around the material that the cell intends to take in. As this pocket deepens, it eventually pinches off, forming a vesicle that transports the material into the cytoplasm of the cell. This mechanism is vital for various functions, including nutrient uptake, immune responses, and the removal of cellular debris.

In contrast, exocytosis involves the expulsion of materials from the cell, where vesicles fuse with the cell membrane to release their contents outside the cell. Diffusion refers to the movement of particles from an area of higher concentration to an area of lower concentration and does not require the cell membrane to change shape. Osmosis is a specific type of diffusion that focuses on the movement of water across a semi-permeable membrane. Therefore, these processes do not involve the cell membrane infolding to intake material, making endocytosis the appropriate choice for this question.