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Tracelet Hopf Algebras and Decomposition Spaces (Extended Abstract) (2105.06186v3)
Published 13 May 2021 in cs.LO and math.CT
Abstract: Tracelets are the intrinsic carriers of causal information in categorical rewriting systems. In this work, we assemble tracelets into a symmetric monoidal decomposition space, inducing a cocommutative Hopf algebra of tracelets. This Hopf algebra captures important combinatorial and algebraic aspects of rewriting theory, and is motivated by applications of its representation theory to stochastic rewriting systems such as chemical reaction networks.