  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.
