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We begin this post by talking about open dynamical systems. Open dynamical systems have been studied extensively within applied category theory (see Myers (2022)), and additionally have been a part of AlgebraicJulia for a while, with AlgebraicDynamics, accompanying blog post.
This is a companion discussion topic for the original entry at https://blog.algebraicjulia.org/post/2023/05/algebraic-geometry-2/