nLab Joachim Kock

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Selected writings

On Frobenius algebras and 2d topological quantum field theory:

• Joachim Kock, Frobenius Algebras and 2d Topological Quantum Field Theories, Cambridge U. Press (2004) [doi:10.1017/CBO9780511615443, webpage, course notes pdf, pdf]

On quantum cohomology:

• Joachim Kock, Israel Vainsencher, An Invitation to Quantum Cohomology – Kontsevich’s Formula for Rational Plane Curves, Birkhäser (2007) [doi:10.1007/978-0-8176-4495-6]

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 7 (2018), 148–192 [arXiv:1510.08934, tac:33-07]

On Petri nets:

• Joachim Kock, Whole-grain Petri nets and processes [arXiv:2005.05108]

See also:

• 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.

On categorified linear algebra with negative and other values:

• Joachim Kock, Jesper Michael Møller, Signs in objective linear algebra, exemplified with exterior powers and determinants [arXiv:2603.19437]

• Joachim Kock, Jesper Michael Møller, Groupoid G-spans and matrices over group rings [arXiv:2603.20787]

For an extension of the counting construction at class equation to a homotopy equivalence of infinity-groupoids see

• Joachim Kock, Thomas Jan Mikhail, Free loop spaces and the Cauchy–Frobenius Lemma [arXiv:2507.01637]

category: people