Categorization is ubiquitous in human cognition and society, and shapes how we perceive and understand the world. Because categories reflect the needs and perspectives of their creators, no category system is entirely objective, and inbuilt biases can have harmful social consequences. Here we propose methods for measuring biases in hierarchical systems of categories, a common form of category organization with multiple levels of abstraction. We illustrate these methods by quantifying the extent to which library classification systems are biased in favour of western concepts and male authors. We analyze a large library data set including more than 3 million books organized into thousands of categories, and find that categories related to religion show greater western bias than do categories related to literature or history, and that books written by men are distributed more broadly across library classification systems than are books written by women. We also find that the Dewey Decimal Classification shows a greater level of bias than does the Library of Congress Classification. Although we focus on library classification as a case study, our methods are general, and can be used to measure biases in both natural and institutional category systems across a range of domains. 1