In this talk, I’ll introduce the formal concept of a (pre)sheaf as data attached to a topological space. Sheaves capture the notion of patching local sources of information to form a global whole, e.g., the binding of visual features such as colour and shape. The formal theory appears to be closely related to the foundational properties asserted by the Information Integration Theory (IIT) for phenomenology. A comparison is intended to engender discussion on ways that phenomenology may benefit from a sheaf theory, or (more generally) a category theory approach.