Sheafification is the process of transforming a presheaf into a sheaf by enforcing the condition of local data being glued together consistently. This concept is vital in sheaf theory, as it allows one to obtain a sheaf that captures the local behavior of a presheaf while ensuring compatibility across open sets. Essentially, sheafification helps in structuring data in a way that respects the topology of the space, making it crucial for understanding both algebraic and topological structures in the study of logic and topoi.
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