ACT Adjoint School

Open Petri nets, mentored by John Baez

• Baez & Pollard, 2017: A compositional framework for reaction networks (doi, arxiv, Azimuth , nCat Cafe )
• Fong, 2015: Decorated cospans (pdf, arxiv, Azimuth , nCat Cafe )

Logic of causality, mentored by Aleks Kissinger

• Kissinger & Uijlen, 2017: A categorical semantics for casual structure (doi, arxiv, Azimuth , nCat Cafe )
• Hensen, Lal, Pusey, 2014: Theory-independent limits on correlations from generalized Bayesian networks (doi, arxiv, Azimuth , nCat Cafe )

Compositional linguistics, mentored by Martha Lewis

• Coecke, Sadrzadeh, Clark, 2010: Mathemical foundations for a compositional distributional model of meaning (arxiv, Azimuth , nCat Cafe )
• Bolt, Coecke, et al, 2017: Interacting conceptual spaces I: Grammatical composition of concepts (arxiv, Azimuth , nCat Cafe )

Open and interconnected systems, mentored by Pawel Sobocinski

• Willems, 2007: The behavioral approach to open and connected systems (doi, Azimuth , nCat Cafe )
• Carboni & Walters, 1987: Cartesian bicategories I (doi, Azimuth , nCat Cafe )

ZX-calculus, mentored by Miriam Backens

• Amy, Chen, Ross, 2017: A finite presentation of CNOT-dihedral operators (doi, arxiv, nCat Cafe )
• Backens, 2014: The ZX-calculus is complete for stabilizer quantum mechanics (doi, arxiv, nCat Cafe )

Partial evaluations, mentored by Tobias Fritz

• Fritz & Perrone, 2018: Monads, partial evaluations, and rewriting (arxiv, slides, nCat Cafe )
• Clementino, Hofmann, Janelidze, 2014: The monads of classical algebra are seldom weakly cartesian (doi, nCat Cafe )
• Trimble, blog post: On the bar construction (1 ,2 )

Turing categories, mentored by Pieter Hofstra

• Cockett & Hofstra, 2008: Introduction to Turing categories (doi, nCat Cafe )
• Cockett, Hofstra, Hrubeš, 2014: Total maps of Turing categories (doi, nCat Cafe )
• Joyal, Street, Verity, 1996: Traced monoidal categories (doi)

Optics and profunctors , mentored by Bartosz Milewski

• Pastro & Street, 2018: Doubles for monoidal categories (pdf, nCat Cafe )

Categorical language models, mentored by Mehrnoosh Sadrzadeh

• Jaeger, 1998: A multi-modal analysis of anaphora and ellipsis (pdf)
• Purver, Cann, Kempson, 2006: Grammars as parsers: Meeting the dialogue challenge (doi, pdf, nCat Cafe )

Mathematics of autopoiesis , mentored by David Spivak

• Fong, Myers, Spivak, 2018: Behavioral mereology (arxiv, nCat Cafe )
• Fong & Spivak, 2019: Graphical regular logic (arxiv, nCat Cafe )
• Luhmann, 2018. Organization and decision (doi)

Dialectica categories of Petri nets, mentored by Valeria de Paiva

• Brown & Gurr, 1990: A categorical linear framework for Petri nets (doi, Azimuth , nCat Cafe )
  • Journal version: Brown & Gurr, 1995: A categorical linear framework for Petri nets (doi)
• de Paiva, 1991: Categorical multirelations, linear logic, and Petri nets (doi, pdf)

Type theory for SMCs, mentored by Michael Shulman

• Shulman, 2021: A practical type theory for symmetric monoidal categories (pdf, arxiv, nCat Cafe )
• Schommer-Pries, 2011: The classification of two-dimensional extended topological field theories (arxiv)

Categories of maintainable relations, mentored by Michael Johnson

• Johnson & Rosebrugh, 2016: Unifying set-based, delta-based and edit-based lenses (pdf)
• Clarke, 2019: Internal lenses as functors and cofunctors (arxiv)

Distances between persistence modules, mentored by Nina Otter

• Bubenik, Scott, Stanley, 2018: Exact weights, path metrics, and algebraic Wasserstein distances (arxiv)
• Harrington, Otter, Schenck, Tillmann, 2019: Stratifying multiparameter persistent homology (doi, arxiv)

Computing with C-sets, mentored by James Fairbanks and Evan Patterson

• Fong, 2015: Decorated cospans (pdf, arxiv, nCat Cafe 1 ,2 ,3 )
• Vagner, Spivak, Lerman, 2015: Algebras of open dynamical systems on the operad of wiring diagrams (pdf, arxiv)

Enriched profunctor nuclei, mentored by Simon Willerton

• Willerton, 2015: The Legendre-Fenchel transform from a category theoretic perspective (arxiv)
• Elliot, 2017, PhD thesis: On the fuzzy concept complex (pdf), Chapters 2-3

Double categories in ACT, mentored by Simona Paoli

• Baez & Courser, 2019: Structured cospans(pdf, arxiv)
• Paoli & Pronk, 2013: A double categorical model of weak 2-categories (pdf, nCat Cafe )
• Paoli, 2019: Simplicial methods for higher categories (doi)

Coalgebraic dynamic logic, mentored by Helle Hvid Hanse and Clemes Kupke

• Rutten 2000: Universal coalgebra: a theory of systems (doi, nCat Cafe )
• Kupke & Pattinson, 2011: Coalgebraic semantics of modal logics: An overview (doi)
• Hansen, Kupke, Leal, 2014: Strong completeness for iteration-free coalgebraic dynamic logics (doi)

Compositional thermostatics, mentored by Spencer Breiner and Joe Moeller

• Baez, Lynch, Moeller, 2021: Compositional thermostatics (arxiv, nCat Cafe )
• Lawvere, 1984: State categories, closed categories, and the existence of semi-continuous entropy functions (pdf)

Fuzzy type theory for opinion dynamics, mentored by Paige North

• Grayson, 2018: An introduction to univalent foundations for mathematicians (doi, nCat Cafe )
• Hansen & Ghrist, 2021: Opinion dynamics on discourse sheaves (doi, arxiv, nCat Cafe )

Compositional timed and probabilistic processes, mentored by Nicoletta Sabadini

• Albasini, Sabadini, Walters, 2011: The compositional construction of Markov processes (nCat cafe )
  • Part I (doi, arxiv)
  • Part II (doi, arxiv)
• Cherubini, Sabadini, Walters, 2004: Timing in the cospan-span model (doi, nCat Cafe )

Algebraic structures in logic and relations, mentored by Filippo Bonchi

• Carboni & Walters, 1987: Cartesian bicategories I (doi)
• Bonchi, Seeber, Sobocinski, 2018: Graphical conjunctive queries (doi, arxiv)
• Bonchi, Pavlovic, Sobocinksi, 2017: Functorial semantics for relational theories (arxiv, nCat Cafe )