All NotesMay 29, 2023Timing monoidal lax categoriesMay 29, 2023The double bicategory of monoidal and bimodular profunctorsMay 29, 2023Spliced arrow polycategoryMay 29, 2023Span(Graph), a Canonical Feedback Algebra of Open Transition Systems (Di Lavore et al)May 29, 2023Promonoidal categoryMay 29, 2023Promonads and String Diagrams for Effectful Categories (Román, 2022)May 29, 2023PromonadMay 29, 2023ProfunctorMay 29, 2023MulticategoryMay 29, 2023Monoidal Streams for Dataflow Programming (Di Lavore, de Felice, Roman, 2022)May 29, 2023Monoidal profunctorMay 29, 2023Markov categoryMay 29, 2023Lax duoidMay 29, 2023DuomulticategoryMay 29, 2023Duoidal categoryMay 29, 2023Contour of a polycategoryMay 29, 2023Contour of a multicategoryMay 29, 2023A Canonical Algebra of Open Transition Systems (Di Lavore et al)May 24, 2023Strong promonadMay 24, 2023State promonadMay 24, 2023Splitting the one-time padMay 24, 2023Profunctor Optics a Categorical Update (Clarke, Elkins, Gibbons, Loregian, Milewski, Pillmore, Román)May 24, 2023Produoidal categoryMay 24, 2023Old - Promonoidal categoryMay 24, 2023Old - Definition of strong promonadMay 24, 2023Monoidal contexts form a categoryMay 24, 2023Mixing normal duoidalsMay 24, 2023Malleable multicategories are promonoidalMay 24, 2023Duoid in a duoidalMay 24, 2023Context theory for categoriesMay 24, 2023CategoryMay 24, 2023Vsquared-categoriesMay 24, 2023String Diagrams for Premonoidal CategoriesMay 24, 2023Spliced arrows form a coherent multicategoryMay 24, 2023Promonoidal category of spliced arrowsMay 24, 2023PosetMay 24, 2023Optics for Premonoidal CategoriesMay 24, 2023Composition of semicartesian Mealy automataMay 24, 2023Comb Diagrams for Discrete-Time FeedbackMay 24, 2023Arrows in HaskellMay 24, 2023A Category of DAGsMay 18, 2023Collages of string diagramsMay 18, 2023Bimodular profunctorMay 18, 2023The 2-category of effectful categoriesMay 18, 2023Strictification of a monoidal functorMay 18, 2023Strictification of a monoidal categoryMay 18, 2023Star-polycategoryMay 18, 2023Slices indexed by spansMay 18, 2023Sliced left adjointMay 18, 2023Quasi 2-adjunctionMay 18, 2023Promonoidals induce coherent multicategoriesMay 18, 2023Promonoidals as multicategories that factorMay 18, 2023PolycategoryMay 18, 2023Not every monoidal functor is naturally isomorphic to a strict oneMay 18, 2023Modules in wire diagramsMay 18, 2023Loop space of a bicategoryMay 18, 2023Linear Logic Without Units (Houston, 2007)May 18, 2023Lax twisted arrow bicategoryMay 18, 2023Kleisli objectMay 18, 2023Kleisli categoryMay 18, 2023Gray monoidMay 18, 2023Free conical cocompletionMay 18, 2023Forgetting about prostarsMay 18, 2023Effectful categoryMay 18, 2023Double categoryMay 18, 2023Do notation is sound and complete for monoidal categoriesMay 18, 2023Comonoids to the leftMay 18, 2023Coherent multicategoryMay 18, 2023Category theoryMay 18, 2023Category enriched in a bicategoryMay 18, 2023Bimodule on a bicategoryMay 18, 2023BicategoryMay 18, 2023Bicategories of processes and lax dinaturalityMay 16, 2023Coherence for monoidal categoriesMay 13, 2023Prolinearly distributive categoryMay 13, 2023OpticsMay 13, 2023NewsMay 13, 20232-Duality, lax and strongMay 3, 2023Viterbi semiringMay 3, 2023Virtual starsMay 3, 2023Transition systems in monoidal streamsMay 3, 2023The adjunction of a lax functor boxMay 3, 2023Symmetric opticsMay 3, 2023Strong monoidal functor boxes in TambaraMay 3, 2023Streams in cartesian monoidal categoriesMay 3, 2023Stream preserves cartesianityMay 3, 2023Stream is a promonadMay 3, 2023Stream functionsMay 3, 2023Stochastic streamsMay 3, 2023Skew promonad of a lax monoidal functorMay 3, 2023SemiringMay 3, 2023Repeated processesMay 3, 2023Reducing an adjunctionMay 3, 2023Reading an example on the monoidal bicategory of profunctorsMay 3, 2023Randomness factorizationMay 3, 2023QuantaleMay 3, 2023Prolinear contourMay 3, 2023Prolinear category of spliced arrowsMay 3, 2023Premonoidal optics may not be a prostrong promonadMay 3, 2023Premonoidal opticsMay 3, 2023Parsing via spliceMay 3, 2023ParsingMay 3, 2023Monoidal streams for Buchi automataMay 3, 2023Monoidal stream computationMay 3, 2023Markov and subMarkov categoriesMay 3, 2023Functor boxMay 3, 2023DisintegrationMay 3, 2023Discrete partial Markov categoryMay 3, 2023Dinaturality for monoidal streamsMay 3, 2023Definitions of combsMay 3, 2023Constructing monoidal stream transducersMay 3, 2023Conditionals in a Markov categoryMay 3, 2023Coinductive streamsMay 3, 2023Coalgebraic stream transducersMay 3, 2023Centre of a monad in SetMay 3, 2023Central product of promonadsMay 3, 2023Automata over a quantaleMay 3, 2023Adamek's theorem for combsMay 3, 2023A Canonical Algebra of Open Transition SystemsApr 12, 2023Linear logicApr 10, 2023Comonads on a cartesian are monoidalApr 10, 2023Commutativity in a map pseudomonoidApr 10, 2023Chu interpretation of linear logicApr 10, 2023Centre of a comonadApr 7, 2023Thickening of a finite functionApr 7, 2023Theory of cartesian multicategoriesApr 7, 2023Simulation simplifies bisimulationApr 7, 2023Raudsilla Seminar, November 2022Apr 7, 2023Quotient of IO transition systemsApr 7, 2023Pseudomonoids in Madj are closed categoriesApr 7, 2023Promonoidal contourApr 7, 2023Produoidal contourApr 7, 2023Parsing vs pretty-printingApr 7, 2023One-time pad protocol session-do implementationApr 7, 2023One-time pad protocolApr 7, 2023Newcombs problemApr 7, 2023Multivariable adjunctionApr 7, 2023Monoidal contexts in grammar ambiguityApr 7, 2023Monoidal categoryApr 7, 2023Lens operationsApr 7, 2023Lawvere theoryApr 7, 2023Faithful cartesian clubApr 7, 2023Exponentiable multicategoryApr 7, 2023Decorating bicategories of processesApr 7, 2023Decategorifying multivariable adjunctionsApr 7, 2023Comagmas in magmasApr 7, 2023Closure of simulation relationApr 7, 2023Cartesian multicategoryApr 7, 2023Bicategories of Processes (Katis, Sabadini, Walters, 1997)Apr 7, 2023Automata as functorsApr 7, 2023AutomataApr 7, 2023An implementation of Newcomb problemMar 7, 2023Unix pipesMar 7, 2023Transformation of cliquesMar 7, 2023The point of coend calculusMar 7, 2023Probabilistic bisimulationMar 7, 2023Pointed profunctorMar 7, 2023Notation for spans, graphicallyMar 7, 2023Normal duoidal categoryMar 7, 2023Moggi effectsMar 7, 2023Lawvere theories and universal modelsMar 7, 2023Jens Seeber on Lawvere theoriesMar 7, 2023Infinity-combsMar 7, 2023Graph diagrams of compact closed categoriesMar 7, 2023Free A-MagmaMar 7, 2023Compact objectMar 7, 2023Combinatorial insertionsMar 7, 2023Building Free Arrows (Sigpfe)Mar 7, 2023A-MagmaMar 7, 2023Switching criterionMar 7, 2023Promonoidal category of opticsMar 7, 2023Open diagrams are pointed profunctorsMar 7, 2023Normalization of profunctors over a monoidal categoryMar 7, 2023Normalization of a produoidalMar 7, 2023Normalization of a duoidal categoryMar 7, 2023Normal duoidals are isomixMar 7, 2023Multiplication of the normalization monadMar 7, 2023Endocells of a map pseudomonoid are duoidalMar 7, 2023Distributive lawMar 7, 2023Categorical Logic (Shulman, 2016)Feb 13, 2023Weakly Distributive Categories (Cockett, Seely, 1997)Feb 13, 2023Twisted arrow pseudomonoidsFeb 13, 2023The 2-Chu-Dialectica Construction and the Polycategory of Multivariable Adjunctions (Shulman, 2020)Feb 13, 2023TCP three way handshakeFeb 13, 2023Session do-notationFeb 13, 2023Quotienting Do-notationFeb 13, 2023Parallax bicategoryFeb 13, 2023Open diagrams are usedFeb 13, 2023Open diagrams appearFeb 13, 2023Motivating normalization of spliceFeb 13, 2023Monoidals parallelizeFeb 13, 2023Mix and isomixFeb 13, 2023Do-notation in type theoryFeb 13, 2023Do-notation compositionFeb 13, 2023Derivations in Do-notationFeb 13, 2023Context theory for monoidal categoriesFeb 13, 2023Being multicategorical in each variable is the Chu constructionFeb 13, 2023Algebra of spliceFeb 13, 2023Feb 7, 2023Terence Tao on writingFeb 7, 2023Produoidal algebra of monoidal contextsFeb 7, 2023Monoidal spliced arrowsFeb 7, 2023Monoidal contextsFeb 7, 2023ModuleFeb 7, 2023Directed acyclic graphFeb 1, 2023Markov as dependency categoriesJan 30, 2023Talk on subdistributionsJan 30, 2023Process theoryJan 30, 2023Non cartesianity in subdistributionsJan 30, 2023Evidential decision theoryJan 30, 2023Cartesian, partial and stochasticJan 30, 2023BisimulationJan 30, 2023Affine Traversals split but whyDec 2, 20221-Dimensional calculusJan 30, 2023Promonoidal category of shufflingsJan 30, 2023Dependence categoryJan 27, 2023Pullbacks preserve colimits in SetJan 27, 2023Posets in duoidalsJan 27, 2023Gaussian probability theoryJan 27, 2023From produoidals to prodependenceJan 27, 2023Conditions on a distributive lawJan 14, 2023Unit of the normalization monadJan 14, 2023Two generals problemJan 14, 2023Symmetric normalization of a produoidalJan 14, 2023Signalling in quantum circuitsJan 14, 2023Regular monoidal languageJan 14, 2023Promonoidal functorJan 14, 2023Produoidal functorJan 14, 2023Prodependence in produoidalsJan 14, 2023Polarized notation for opticsJan 14, 2023Monoidal width as a duoidal functorJan 14, 2023Formal normalizationJan 14, 2023Eilenberg-Moore objectJan 14, 2023Dependence from duoidalsJan 14, 2023Buchi monoidal streamsJan 14, 2023Algebras of normalization are normal produoidalsJan 14, 2023A good stochastic example of opticsJan 14, 2023Nov 27, 2022Tambara modules as algebrasNov 27, 2022Tambara moduleNov 27, 2022Signalling in quantum circuitsNov 27, 2022Open internal diagramsNov 27, 2022Monoids and comonoidsNov 27, 2022Map pseudomonoidNov 27, 2022Decomposition complexityNov 27, 2022Continuation monadNov 27, 2022Compositional dependencies with duoidalsNov 27, 2022Composition along a channelNov 27, 2022ComomonoidNov 27, 2022Bimonoid in a duoidalNov 22, 2022XOR variable exchangeNov 22, 2022Signalling structure of process theoriesNov 22, 2022Polycategory of multivariable adjunctionsNov 22, 2022Mates correspondenceNov 22, 2022Lax pseudofrobenius algebraNov 22, 2022Convolution and coconvolutionNov 22, 2022Beck-Chevalley conditionNov 21, 2022Subdistribution monadNov 21, 2022Strings for duoidal categoriesNov 21, 2022PseudomonoidNov 21, 2022Observations and comparatorsNov 21, 2022Monty-Hall in partial MarkovNov 21, 2022Module categoryNov 21, 2022Duoidal TambaraNov 21, 2022Bimodular tambaraNov 21, 2022Bayes update on subdistributionsNov 7, 2022Synthetic Bayes theoremNov 7, 2022Strong symmetric monoidal functorNov 7, 2022Spliced arrows vs opticsNov 7, 2022Separatedness, discreteness, and comparatorsNov 7, 2022Reading Bayesian inversion diagramsNov 7, 2022Modelling Newcomb problemNov 7, 2022Markov by splitNov 7, 2022Conditionals of a familyNov 7, 2022Categories are monoids in Span(Set)Nov 7, 2022Building distributions that are marginally independent of the parameterNov 4, 2022Two tensors, three dimensionsNov 4, 2022TraversablesNov 4, 2022Taking runtime seriouslyNov 4, 2022Strong monadNov 4, 2022Reversors in profunctorsNov 4, 2022Prostrong promonadNov 4, 2022Prostrong monadNov 4, 2022Proeffectful categoriesNov 4, 2022PrepromonoidalityNov 4, 2022Philosophy of linear foundationsNov 4, 2022Note IndexNov 4, 2022Newcomb's Problem and Two Principles of Choice (Nozick 1969)Nov 4, 2022Freyd categoryNov 4, 2022Do notation for strong monadsNov 4, 2022Diagrams of prostrengthNov 4, 2022Death in DamascusNov 4, 2022Compatible squares of functor lensesNov 4, 2022Companions and conjointsNov 4, 2022ComonadNov 4, 2022Combunication, an ideaNov 4, 2022Coalgebras of shape and contentsNov 4, 2022Coalgebra of the real intervalOct 6, 2022Split runtimeOct 6, 2022Premonoidal functorOct 6, 2022PolygraphOct 6, 2022Monad properties via do notationOct 6, 2022Free effectful category IOct 6, 2022Citing these notesOct 6, 2022Bayesian Inversion in Partial MarkovOct 4, 2022While loops as tracesOct 4, 2022What is special about Set, in the double category CatOct 4, 2022Weighted colimits in box notationOct 4, 2022Van Laarhoven lenses and gratesOct 4, 2022Values and computationOct 4, 2022Unnatural transformationsOct 4, 2022Uniform copy deleteOct 4, 2022Unbiased premonoidalOct 4, 2022Type Theory for unbiased monoidal categoriesOct 4, 2022Type theory for symmetric monoidal categoriesOct 4, 2022Type theory for delayed feedbackOct 4, 2022Type theory for a strong monoidal endofunctorOct 4, 2022Twisted monoidsOct 4, 2022Towards linear mathematicsOct 4, 2022Three notations for symmetric monoidal categoriesOct 4, 2022Three equalities for combs and opticsOct 4, 2022Three criteria for truthOct 4, 2022The Stream(-) constructionOct 4, 2022The stream endofunctor has a terminal coalgebraOct 4, 2022The idea of shape-contentsOct 4, 2022The 2-Polycategorical structure of MadjOct 4, 2022Tensor of bimodular categoriesOct 4, 2022TabulatorOct 4, 2022Sync-minimal lens spanOct 4, 2022Switchings of a linkingOct 4, 2022Surjections of automata are quotientsOct 4, 2022Surface diagrams for pseudofunctorsOct 4, 2022SuplatticeOct 4, 2022Subtle non-implication in corneringsOct 4, 2022String diagrams for monad and monad algebrasOct 4, 2022String diagrams for category theoryOct 4, 2022Stream programming and signal flowOct 4, 2022Stream programming and monoidal categoriesOct 4, 2022Stochastic to stream is well-definedOct 4, 2022Stochastic streams via Adamek's theoremOct 4, 2022Stochastic processes via streamsOct 4, 2022Star-autonomous categoryOct 4, 2022Some dependent lensesOct 4, 2022Smoking lesion problemOct 4, 2022Slice categories as categories of coalgebrasOct 4, 2022Sleeping beauty problemOct 4, 2022Shape and contents comonadOct 4, 2022Sets is a monoidal categoryOct 4, 2022Sesquifunctors and the funny tensor productOct 4, 2022Runtime monoidal categoryOct 4, 2022Right adjoint to oplax is laxOct 4, 2022Refining Fox's TheoremOct 4, 2022Reduction in symmetric monoidal categoriesOct 4, 2022Range with total compositionOct 4, 2022Quoting comonad of a monadOct 4, 2022Quotient transition systemOct 4, 2022Putting an end to parameters IVOct 4, 2022Putting an end to parameters IIIOct 4, 2022Putting an end to parameters IIOct 4, 2022Putting an end to parameters IOct 4, 2022Pure tensor of promonadsOct 4, 2022Pseudomonoid lax homomorphismOct 4, 2022Proxy-pullback squareOct 4, 2022Promonoids from monoidsOct 4, 2022Promonads are id-on-objects functorsOct 4, 2022Probabilistic mixtures as promonoidalsOct 4, 2022Partial leaf functionsOct 4, 2022Parameterised monadsOct 4, 2022Parameterised comonadsOct 4, 2022Opmonoidal comonadOct 4, 2022Operational view of gratesOct 4, 2022Lax opticsOct 4, 2022On syntax and free objectsOct 4, 2022Notation for total compositionOct 4, 2022Notation for spansOct 4, 2022Near ringsOct 4, 2022Motivation in the cartesian streamsOct 4, 2022Motivating bicategoriesOct 4, 2022Monoids on the arrow categoryOct 4, 2022Monoidals inside CatOct 4, 2022Monoidal streams via actionsOct 4, 2022Monoidal stream computation IIOct 4, 2022Monoidal profunctors (string diagrams)Oct 4, 2022Monoidal double category of categoriesOct 4, 2022Monoidal category of streamsOct 4, 2022Milewski-Vertechi dependent opticsOct 4, 2022Metric spaceOct 4, 2022Map pseudomonoid mapsOct 4, 2022Lukasiewicz LogicOct 4, 2022Loose monoid in a double categoryOct 4, 2022Loose bicategory of a double categoryOct 4, 2022List opmonoidal comonadOct 4, 2022Linear solution for the barberOct 4, 2022Lenses flowing backOct 4, 2022Lax twisted monoids and convolutionOct 4, 2022Kl(D) is not pseudopurifiableOct 4, 2022Interchange lawOct 4, 2022Interaction lawsOct 4, 2022Integral in a bialgebraOct 4, 2022Independent marginalization for a strong monadOct 4, 2022Hopf AlgebrasOct 4, 2022Homomorphisms of promonads are functor squaresOct 4, 2022Has constructivism failed?Oct 4, 2022Hacking dependent lenses as mixed opticsOct 4, 2022Grothendieck constructionOct 4, 2022Graphical Language with Delayed Trace (Carette, de Visme, Perdrix, 2021)Oct 4, 2022Graphical closed monoidalsOct 4, 2022Graphical calculus for madjOct 4, 2022Funny tensor of promonadsOct 4, 2022Funny tensor as coproductOct 4, 2022Functor boxes in CatOct 4, 2022Functional Decision Theory. A New Theory of Instrumental Rationality (Yudkowsky, Soares, 2018)Oct 4, 2022From stateful morphisms to streamsOct 4, 2022Freyd as pseudomonoidsOct 4, 2022Fox's theorem and cocommutativityOct 4, 2022Feedback premonoidal categoryOct 4, 2022Feedback in compact bicategoriesOct 4, 2022Examples of monoidal categoryOct 4, 2022Essentially algebraic theoriesOct 4, 2022End-preserving functorsOct 4, 2022Effects of a monadOct 4, 2022Drawing the Church booleansOct 4, 2022Double category CATOct 4, 2022Discardable monads and marginalizationOct 4, 2022Directed acyclic open hypergraphsOct 4, 2022Dioptics from corners in both boundariesOct 4, 2022DiopticsOct 4, 2022Diagrammatic formal dualitiesOct 4, 2022Dependent optics (Riley)Oct 4, 2022Definitions of topologyOct 4, 2022Corresponding graphs for stateful spansOct 4, 2022Copartial functionsOct 4, 2022Constructivism in Computer Science and category theoryOct 4, 2022Constructive mathematicsOct 4, 2022Constructing monoidal stream transducers IIOct 4, 2022Constructing a theory of processesOct 4, 2022Composition of stateful spansOct 4, 2022Composing stateful spansOct 4, 2022Combs as final coalgebrasOct 4, 2022Components of the monoidal bicategory of profunctorsOct 4, 2022Companions in a double categoryOct 4, 2022Compact closed streams via Adamek's theoremOct 4, 2022Coloring premonoidalityOct 4, 2022Coinductively defined streamsOct 4, 2022Coinductive cellular automataOct 4, 2022Cofunctors and lensesOct 4, 2022Causality in two boundariesOct 4, 2022Categorical Composable Cryptography (Broadbent and Karvonen, 2021)Oct 4, 2022Cartesian streams via Adamek's theoremOct 4, 2022Cartesian stream transducersOct 4, 2022Cartesian Categories are monoidalOct 4, 2022Cartesian Categories and comonoidsOct 4, 2022Cartesian by splitOct 4, 2022Braided monoidal categoryOct 4, 2022Braid clique in MonRunOct 4, 2022Boxes are bubblesOct 4, 2022Binoidal and Premonoidal CategoriesOct 4, 2022Bimonoidal categoryOct 4, 2022Bimodular categoriesOct 4, 2022Bayes update with do-notationOct 4, 2022Bayes rare illness testingOct 4, 2022Attack modelsOct 4, 2022Applying Adamek in SetOct 4, 2022Algebraically complete categoriesOct 4, 2022Adjunctions in a proarrow equipmentOct 4, 2022Accessible categoriesOct 3, 2022The Structure of Concurrent Process Histories (Nester, 2020)Oct 3, 2022Synchronous StreamsOct 3, 2022Sur la Commutation des Limites (Foltz, 1981)Oct 3, 2022Strict monoidal categories and coherenceOct 3, 2022Simple type theoryOct 3, 2022Resumption monadOct 3, 2022Quantum combsOct 3, 2022PromonoidOct 3, 2022ProcessesOct 3, 2022ProbabilityOct 3, 2022Presenting linear mathematics IIOct 3, 2022Presenting linear mathematics IOct 3, 2022Premonoidal categoryOct 3, 2022Premonoidal Categories and a Graphical View of Programs (Jeffrey, 1998)Oct 3, 2022Motivating monoidal categoriesOct 3, 2022Monoids and promonoidsOct 3, 2022MonadOct 3, 2022Locally Accessible and Presentable Categories (Adamek, Rosicky, 1994)Oct 3, 2022Linear mathematicsOct 3, 2022EffectusOct 3, 2022Effect MonoidOct 3, 2022Effect algebraOct 3, 2022Duals and compact closed categoriesOct 3, 2022DualitiesOct 3, 2022Dependent lensesOct 3, 2022Dataflow programmingOct 3, 2022An Introduction to Locally Finitely Presentable Categories (Sarazola, 2017)Oct 3, 2022Algebra of partial and copartialOct 3, 2022A Classification of Accessible Categories (Adamek, Borceux, Lack, Rosicky, 2002)UnknownThe Produoidal Algebra of Process Decomposition (Earnshaw, Hefford, Román, 2023)UnknownRésuméUnknownOpen Diagrams via Coend Calculus (Román, 2020)UnknownModels of Programming Languages (Melliès)UnknownMikrokosmos: an Educational Lambda Interpreter (Román, 2018)UnknownEvidential Decision Theory via Partial Markov Categories (Di Lavore, Román)UnknownCornering Optics (Boisseau, Nester, Román, 2022)