Compositionality

The open-access journal for the mathematics of composition

Compositionality describes and quantifies how complex things can be assembled out of simpler parts.

Compositionality (ISSN 2631-4444) is an open-access, arXiv-overlay journal for research using compositional ideas in any discipline. For more information, see About.

VOLUME 6 (2024)

Issue 1: Profunctor Optics, a Categorical Update

Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore, and Mario Román

VOLUME 5 (2023)

Issue 10: Traced Monads and Hopf Monads

Masahito Hasegawa and Jean-Simon Pacaud Lemay

Issue 9: Bayesian open games

Joe Bolt, Jules Hedges, and Philipp Zahn

Issue 8: Substructural fixed-point theorems and the diagonal argument: theme and variations

David Michael Roberts

Issue 7: Monotones in General Resource Theories

Tomáš Gonda and Robert W. Spekkens

Issue 6: Degrees in random $m$-ary hooking networks

Kiran R. Bhutani, Ravi Kalpathy, and Hosam Mahmoud

Issue 5: Completeness of the ZH-calculus

Miriam Backens, Aleks Kissinger, Hector Miller-Bakewell, John van de Wetering, and Sal Wolffs

Issue 4: Koszul duality for operadic categories

Michael Batanin and Martin Markl

Issue 3: Operadic categories as a natural environment for Koszul duality

Michael Batanin and Martin Markl

Issue 2: Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality

Lachlan McPheat, Mehrnoosh Sadrzadeh, Hadi Wazni, and Gijs Wijnholds

Issue 1: Toposes of Topological Monoid Actions

Morgan Rogers

VOLUME 4 (2022)

Issue 5: Categorical Data Structures for Technical Computing

Evan Patterson, Owen Lynch, and James Fairbanks

Issue 4: Urns & Tubes

Bart Jacobs

Issue 3: Structured versus Decorated Cospans

John C. Baez, Kenny Courser, and Christina Vasilakopoulou

Issue 2: Coherence for adjunctions in a 3-category via string diagrams

Manuel Araújo

Issue 1: Lambek pregroups are Frobenius spiders in preorders

Dusko Pavlovic

VOLUME 3 (2021)

Issue 4: Language Modeling with Reduced Densities

Tai-Danae Bradley and Yiannis Vlassopoulos

Issue 3: Homotopy theory of Moore flows (I)

Philippe Gaucher

Issue 2: Compositionality of Rewriting Rules with Conditions

Nicolas Behr and Jean Krivine

Issue 1: Categorical Stochastic Processes and Likelihood

Dan Shiebler

VOLUME 2 (2020)

Issue 4: Closing the category of finitely presented functors under images made constructive

Sebastian Posur

Issue 3: Infinite products and zero-one laws in categorical probability

Tobias Fritz and Eigil Fjeldgren Rischel

Issue 2: Assignments to sheaves of pseudometric spaces

Michael Robinson

Issue 1: Distributive laws for Lawvere theories

Eugenia Cheng

VOLUME 1 (2019)

Issue 4: Network models from Petri nets with catalysts

John C. Baez, John Foley, and Joe Moeller

Issue 3: Fuzzy sets and presheaves

John F. Jardine

Issue 2: Stinespring’s construction as an adjunction

Arthur J. Parzygnat

Issue 1: An effect-theoretic reconstruction of quantum theory

John van de Wetering

To appear:

Manin and Marcolli - Homotopy Theoretic and Categorical Models of Neural Information Networks (arXiv).
Aduddell, Fairbanks, Kumar, Ocal, Patterson, and Shapiro - A compositional account of motifs, mechanisms, and dynamics in biochemical regulatory networks (arXiv).