On Frobenius algebras and 2d topological quantum field theory:
Proving the biequivalence between Feynman categories and colored operads:
Michael Batanin, Joachim Kock, Mark Weber, Regular patterns, substitudes, Feynman categories and operads, Theory Appl. Categ. 33 (2018), 148–192 (arXiv:1510.08934)
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks, Homotopy linear algebra. Proc. Roy. Soc. Edinburgh Sect. A, 148(2):293–325, 2018 (arXiv:1602.05082).
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks, Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees. Adv. Math., 254:79–117, 2014.
David Gepner, Rune Haugseng, Joachim Kock, ∞-Operads as analytic monads, (arXiv:1712.06469)
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks, Decomposition spaces, incidence algebras and Möbius inversion, arXiv:1404.3202
Nicolas Behr, Joachim Kock, Tracelet Hopf algebras and decomposition spaces, arXiv:2105.06186
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.
Last revised on August 10, 2023 at 12:01:25. See the history of this page for a list of all contributions to it.