Categorization is ubiquitous in human cognition and society, and impacts how we perceive and understand the world. In reflecting the needs and perspectives of their creators, no categorization system is entirely objective, and inbuilt biases can have harmful social consequences. Here, we propose methods for quantifying three kinds of category biases in hierarchical category systems. We present a study on two widely used library classification systems (the DDC and LCC) as large-scale examples of human categorization, and use our methods to quantify bias towards content associated with western (vs non-western) concepts in topic areas including history and religion. We find consistent evidence for western bias and show that the DDC tends to exhibit more western bias than the LCC. Our methods are general, and can be used to survey biases across topic areas, bias attributes, and hierarchical category systems.