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Tracelets are the intrinsic carriers of causal information in categoricalrewriting systems. In this work, we assemble tracelets into a symmetricmonoidal decomposition space, inducing a cocommutative Hopf algebra oftracelets. This Hopf algebra captures important combinatorial and algebraicaspects of rewriting theory, and is motivated by applications of itsrepresentation theory to stochastic rewriting systems such as chemical reactionnetworks.

Tracelet Hopf Algebras and Decomposition Spaces (Extended Abstract)