Explore data complexes and their role in semi-automated data-alignment tools for commercial database software in this 54-minute lecture. Delve into the theory behind topological obstructions in database JOIN operations, learn how to detect these obstructions using obstruction cocycles, and understand the concept of persistence level in database collections. Examine the model category of data complexes, including morphisms, homotopy, and homology, and their application in measuring obstructions to finding measures on product spaces. Discover the compatibility of obstruction theory with a fibrant filtration built from the Wasserstein distance on measures. Cover topics such as global obstructions, applied math in database engineering, combinatorics, data tables, extension problems, data subcomplexes, and the Second Fundamental Theorem. Conclude with a discussion on local and global costs in database joins and homotopic groups.