Topos Institute

Topos Institute is a non-profit organization that specializes in advanced mathematical research and software development, particularly in the areas of applied category theory, mathematical logic, and artificial intelligence. Registered to receive federal awards since April 2020, Topos Institute has been awarded multiple project grants from defense-related agencies, primarily the Air Force Research Laboratory. The institute's work focuses on developing innovative mathematical approaches and computational tools to solve complex problems in science and engineering, with applications relevant to both academic and industry needs.

Through its federal grant awards and sub-awards, Topos Institute has engaged in a diverse range of projects. These include research on polynomial functors, the structure and dynamics of working language, and functorial semantics for statistical theories and models. The institute has also developed computational design environments for functorial dynamics and interaction. Notably, Topos Institute has participated in DARPA's Automating Scientific Knowledge Extraction and Modeling (ASKEM) program as a sub-awardee to the University of Florida. In this capacity, they have contributed to tasks such as model ingestion, spatial modeling for space weather, modeling workflow management, and model verification systems. Their work involves creating open-source software, developing mathematical frameworks, and integrating complex modeling capabilities. The primary funding agencies for these projects have been the Air Force Research Laboratory and, indirectly through sub-awards, DARPA. Additionally, Topos Institute received support from the National Science Foundation's Division of Mathematical Sciences to organize the Adjoint School, an international training program for new researchers in applied category theory.