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.

翻译：线条是绝对重写系统中因果关系信息的内在载体。 在这项工作中,我们将微粒聚集到一个对称的单亚化分解空间中,引致微粒的混合式Hopf代数。 这个Hopf代数采集了重写理论的重要组合和代数方面,其动机是将其代表理论应用于化学反应网络等随机重写系统。