While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -- the ability to reason with high-level interfaces and reusable structures central to modern mathematics and software engineering. We introduce LeanCat, a challenging benchmark comprising 100 fully formalized category-theory tasks in Lean. Unlike algebra or arithmetic, category theory serves as a rigorous stress test for structural, interface-level reasoning. Our evaluation reveals a severe abstraction gap: the best state-of-the-art model solves only 12.0% of tasks at pass@4, with performance collapsing from 55.0% on Easy tasks to 0.0% on High-difficulty tasks, highlighting a failure in compositional generalization. To overcome this, we evaluate LeanBridge, a retrieval-augmented agent that employs a retrieve-generate-verify loop. LeanBridge achieves a peak success rate of 24.0% -- doubling the performance of the best static baseline. These results empirically demonstrate that iterative refinement and dynamic library retrieval are not merely optimizations but strict necessities for neuro-symbolic reasoning in abstract domains. LeanCat offers a compact, reusable testbed for tracking progress toward reliable, research-level formalization.
@article{arxiv.2512.24796,
title = {LeanCat: A Benchmark Suite for Formal Category Theory in Lean (Part I: 1-Categories)},
author = {Rongge Xu and Hui Dai and Yiming Fu and Jiedong Jiang and Tianjiao Nie and Junkai Wang and Holiverse Yang and Zhi-Hao Zhang},
journal= {arXiv preprint arXiv:2512.24796},
year = {2026}
}