Worked on the agda/agda-categories repository to formalize pushout colimits, delivering a foundational feature for category theory libraries. The approach involved constructing rigorous formal proofs in Agda, leveraging expertise in type theory and formal methods to ensure correctness and maintainability. By integrating these proofs directly into the codebase, the work strengthened the theoretical underpinnings of the library and enabled more reliable higher-level constructions for downstream users. This contribution addressed a core need for categorical tooling, laying the groundwork for future extensions and improving confidence in the library’s correctness. The work focused on depth and precision rather than breadth or bug fixes.