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April 5, 2026Open Access

Homotopy Data for Quillen's Theorem A: Galois Connections in Lean 4

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Key Points

To formalize Quillen's Theorem A for Galois connections between partial orders using Lean 4.
Developed machine-checked formalization of Galois connections.
Constructed forward and backward nerve maps with explicit 1-simplices.
Established fiber contractibility related to Quillen's theorem.
Proved that the nerve of any category with a terminal object is connected.
Demonstrated unique edges to the terminal vertex in the constructed simplicial set.

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Implication

Formalization shows homotopy connectivity in partial orders for Galois connections, indicating foundational insights into category theory.

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Cite This Study

Nova Spivack (2026) studied this question.

synapsesocial.com/papers/69d894ad6c1944d70ce05a5e https://doi.org/10.5281/zenodo.19460385

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