Large language models (LLMs) such as ChatGPT are increasingly proficient in understanding and generating a mixture of code and text. Evaluation based on such \emph{mixture} can lead to a more comprehensive understanding of the models' abilities in solving coding problems. However, in this context, current evaluation methods are either limited in task coverage or lack standardization. To address this issue, we propose using category theory as a framework for evaluation. Specifically, morphisms within a code category can represent code debugging and transformation, functors between two categories represent code translation, and functors between a code category and a natural language category represent code generation, explanation, and reproduction. We present an automatic evaluation framework called \textbf{CatCode} (\textbf{Cat}egory \textbf{Code}) that can comprehensively assess the coding abilities of LLMs, including ChatGPT, Text-Davinci, and CodeGeeX.