J. C. Baez, B. Fong & B. S. Pollard (2016):
A compositional framework for Markov processes.
Journal of Mathematical Physics 57(3),
doi:10.1063/1.4941578.
J. Bénabou (1967):
Introduction to bicategories.
In: Reports of the Midwest Category Seminar.
Springer Berlin Heidelberg,
Berlin, Heidelberg,
pp. 1–77,
doi:10.1007/BFb0074299.
S. Castellan, P. Clairambault, S. Rideau & G. Winskel (2017):
Games and Strategies as Event Structures.
Logical Methods in Computer Science Volume 13, Issue 3,
doi:10.23638/LMCS-13(3:35)2017.
Alexander S Corner (2016):
Day convolution for monoidal bicategories.
University of Sheffield.
G. S. H. Cruttwell, B. Gavranovi\'c, N. Ghani, P. Wilson & F. Zanasi (2022):
Categorical Foundations of Gradient-Based Learning.
In: Programming Languages and Systems,
doi:10.1007/978-3-030-99336-8_1.
J. L. Fiadeiro & V. Schmitt (2007):
Structured Co-spans: An Algebra of Interaction Protocols.
In: Algebra and Coalgebra in Computer Science,
pp. 194–208,
doi:10.1007/978-3-540-73859-6_14.
M. Fiore, N. Gambino, M. Hyland & G. Winskel (2007):
The cartesian closed bicategory of generalised species of structures.
Journal of the London Mathematical Society 77(1),
pp. 203–220,
doi:10.1112/jlms/jdm096.
M. Fiore & P. Saville (2019):
A type theory for cartesian closed bicategories.
In: 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS),
doi:10.1109/LICS.2019.8785708.
B. Fong, D. Spivak & R. Tuyeras (2019):
Backprop as Functor: A compositional perspective on supervised learning.
In: 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS),
doi:10.1109/lics.2019.8785665.
M. Gaboardi, S. Katsumata, D. Orchard & T. Sato (2021):
Graded Hoare Logic and its Categorical Semantics.
In: Programming Languages and Systems,
pp. 234–263,
doi:10.1007/978-3-030-72019-3_9.
Z. Galal (2020):
A Profunctorial Scott Semantics.
In: 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020),
doi:10.4230/LIPICS.FSCD.2020.16.
F. R. Genovese, J. Herold, F. Loregian & D. Palombi (2021):
A Categorical Semantics for Hierarchical Petri Nets.
Electronic Proceedings in Theoretical Computer Science 350,
pp. 51–68,
doi:10.4204/eptcs.350.4.
R. Gordon, A. J. Power & R. Street (1995):
Coherence for tricategories.
Memoirs of the American Mathematical Society,
doi:10.1090/memo/0558.
N. Gurski (2013):
Coherence in Three-Dimensional Category Theory.
Cambridge University Press,
doi:10.1017/CBO9781139542333.
N. Gurski & A. Osorno (2013):
Infinite loop spaces, and coherence for symmetric monoidal bicategories.
Advances in Mathematics 246,
pp. 1 – 32,
doi:10.1016/j.aim.2013.06.028.
C. Heunen & B. Jacobs (2006):
Arrows, like Monads, are Monoids.
In: 22nd Annual Conference on Mathematical Foundations of Programming Semantics (MFPS),
doi:10.1016/j.entcs.2006.04.012.
B. P. Hilken (1996):
Towards a proof theory of rewriting: the simply typed 2λ-calculus.
Theoretical Computer Science 170(1),
pp. 407–444,
doi:10.1016/S0304-3975(96)80713-4.
T. Hirschowitz (2013):
Cartesian closed 2-categories and permutation equivalence in higher-order rewriting.
Logical Methods in Computer Science 9,
pp. 1–22,
doi:10.2168/LMCS-9(3:10)2013.
G. Janelidze & G. M. Kelly (2001):
A note on actions of a monoidal category.
Theory and Applications of Categories 9(4),
pp. 61–91.
Available at tac.mta.ca/tac/volumes/9/n4/n4.pdf..
A. Jeffrey (1997):
Premonoidal categories and a graphical view of programs.
S. Katsumata (2014):
Parametric effect monads and semantics of effect systems.
In: 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL),
doi:10.1145/2535838.2535846.
A. Kerinec, G. Manzonetto & F. Olimpieri (2023):
Why Are Proofs Relevant in Proof-Relevant Models?.
Proceedings of the ACM on Programming Languages (POPL),
doi:10.1145/3571201.
S. Lack (2008):
Icons.
Applied Categorical Structures 18(3),
pp. 289–307,
doi:10.1007/s10485-008-9136-5.
T. Leinster (2004):
Higher operads, higher categories.
London Mathematical Society Lecture Note Series 298.
Cambridge University Press,
doi:10.1017/CBO9780511525896.
P. B. Levy (2003):
Call-By-Push-Value: A Functional/Imperative Synthesis.
Springer Netherlands,
doi:10.1007/978-94-007-0954-6.
P. B. Levy, J. Power & H. Thielecke (2003):
Modelling environments in call-by-value programming languages.
Information and Computation 185(2),
pp. 182–210,
doi:10.1016/s0890-5401(03)00088-9.
S. Mac Lane & R. Paré (1985):
Coherence for bicategories and indexed categories.
Journal of Pure and Applied Algebra 37,
pp. 59 – 80,
doi:10.1016/0022-4049(85)90087-8.
D. McDermott & T. Uustalu (2022):
Flexibly Graded Monads and Graded Algebras.
In: Lecture Notes in Computer Science.
Springer International Publishing,
pp. 102–128,
doi:10.1007/978-3-031-16912-0_4.
D. McDermott & T. Uustalu (2022):
What Makes a Strong Monad?.
Electronic Proceedings in Theoretical Computer Science 360,
pp. 113–133,
doi:10.4204/eptcs.360.6.
P.-A. Melliès (2012):
Parametric monads and enriched adjunctions.
Available at https://www.irif.fr/~mellies/tensorial-logic/8-parametric-monads-and-enriched-adjunctions.pdf..
P.-A. Melliès (2021):
Asynchronous Template Games and the Gray Tensor Product of 2-Categories.
In: 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS),
doi:10.1109/lics52264.2021.9470758.
E. Moggi (1989):
Computational lambda-calculus and monads.
In: Proceedings, Fourth Annual Symposium on Logic in Computer Science.
IEEE Comput. Soc. Press,
doi:10.1109/lics.1989.39155.
E. Moggi (1991):
Notions of computation and monads.
Information and Computation 93(1),
pp. 55–92,
doi:10.1016/0890-5401(91)90052-4.
F. Olimpieri (2021):
Intersection Type Distributors.
In: 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS),
doi:10.1109/lics52264.2021.9470617.
H. Paquet & P. Saville (2023):
Strong pseudomonads and premonoidal bicategories.
ArXiv:2304.11014.
J. Power (2002):
Premonoidal categories as categories with algebraic structure.
Theoretical Computer Science 278(1-2),
pp. 303–321,
doi:10.1016/s0304-3975(00)00340-6.
J. Power & E. Robinson (1997):
Premonoidal categories and notions of computation.
Mathematical Structures in Computer Science 7(5),
pp. 453–468,
doi:10.1017/s0960129597002375.
J. Power & H. Thielecke (1997):
Environments, continuation semantics and indexed categories.
In: Lecture Notes in Computer Science.
Springer Berlin Heidelberg,
pp. 391–414,
doi:10.1007/bfb0014560.
M. Román (2022):
Promonads and String Diagrams for Effectful Categories.
CoRR abs/2205.07664,
doi:10.48550/arXiv.2205.07664.
ArXiv:2205.07664.
C. J. Schommer-Pries (2009):
The Classification of Two-Dimensional Extended Topological Field Theories.
University of California.
Available at https://arxiv.org/pdf/1112.1000.pdf.
R. A. G. Seely (1987):
Modelling Computations: A 2-Categorical Framework.
In: 2nd Annual IEEE Symp. on Logic in Computer Science (LICS).
A. Slattery (2023):
Pseudocommutativity and Lax Idempotency for Relative Pseudomonads.
ArXiv:2304.14788.
A. L. Smirnov (2008):
Graded monads and rings of polynomials.
Journal of Mathematical Sciences 151(3),
pp. 3032–3051,
doi:10.1007/s10958-008-9013-7.
S. Staton (2017):
Commutative Semantics for Probabilistic Programming.
In: Programming Languages and Systems.
Springer Berlin Heidelberg,
pp. 855–879,
doi:10.1007/978-3-662-54434-1_32.
H. Thielecke (1997):
Continuation Semantics and Self-adjointness.
Electronic Notes in Theoretical Computer Science 6,
pp. 348–364,
doi:10.1016/s1571-0661(05)80149-5.
T. Tsukada, K. Asada & C.-H. L. Ong (2018):
Species, Profunctors and Taylor Expansion Weighted by SMCC.
In: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS),
doi:10.1145/3209108.3209157.
L. Wester Hansen & M. Shulman (2019):
Constructing symmetric monoidal bicategories functorially.
ArXiv:1910.09240.