LeanCat: A Benchmark Suite for Formal Category Theory in Lean (Part I: 1-Categories)

• URL: http://arxiv.org/abs/2512.24796v1
• Date: Wed, 31 Dec 2025 11:33:29 GMT
• Title: LeanCat: A Benchmark Suite for Formal Category Theory in Lean (Part I: 1-Categories)
• Abstract summary: LeanCat is a Lean benchmark for category-theoretic formalization.<n>Part I: 1-Categories contains 100 fully formalized statement-level tasks.<n>Part II: LeanBridge uses LeanExplore to search Mathlib and observe consistent gains over single-model baselines.
• Score: 7.871706113805829
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models (LLMs) have made rapid progress in formal theorem proving, yet current benchmarks under-measure the kind of abstraction and library-mediated reasoning that organizes modern mathematics. In parallel with FATE's emphasis on frontier algebra, we introduce LeanCat, a Lean benchmark for category-theoretic formalization -- a unifying language for mathematical structure and a core layer of modern proof engineering -- serving as a stress test of structural, interface-level reasoning. Part I: 1-Categories contains 100 fully formalized statement-level tasks, curated into topic families and three difficulty tiers via an LLM-assisted + human grading process. The best model solves 8.25% of tasks at pass@1 (32.50%/4.17%/0.00% by Easy/Medium/High) and 12.00% at pass@4 (50.00%/4.76%/0.00%). We also evaluate LeanBridge which use LeanExplore to search Mathlib, and observe consistent gains over single-model baselines. LeanCat is intended as a compact, reusable checkpoint for tracking both AI and human progress toward reliable, research-level formalization in Lean.

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