Thinking·OS

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Explore the knowledge graph

Adjunction depends on Functor. Activate to inspect this relation.Axiom of choice depends on Function. Activate to inspect this relation.Cartesian coordinate system enables Function. Activate to inspect this relation.Category theory applies to Function. Activate to inspect this relation.Continuous function is a Function. Activate to inspect this relation.Dynamical systems applies to Function. Activate to inspect this relation.Fourier analysis applies to Function. Activate to inspect this relation.Function is a Relation. Activate to inspect this relation.Function composition applies to Function. Activate to inspect this relation.Function depends on Set. Activate to inspect this relation.Function depends on Variable. Activate to inspect this relation.Functor applies to Category. Activate to inspect this relation.Functor applies to Category. Activate to inspect this relation.Isomorphism is a Morphism. Activate to inspect this relation.Monad is a Functor. Activate to inspect this relation.Morphism is part of Category. Activate to inspect this relation.Morphism is analogous to Function. Activate to inspect this relation.Morphism is part of Category. Activate to inspect this relation.Natural Transformation depends on Functor. Activate to inspect this relation.Random variable is a Variable. Activate to inspect this relation.Sine and cosine is a Function. Activate to inspect this relation.Yoneda Lemma applies to Functor. Activate to inspect this relation.MorphismCategoryFunctionCategoryIsomorphismFunctorVariableRelationAxiom of choiceCategory theoryContinuous functionDynamical systemsFourier analysisSetCartesian coordinate systemFunction compositionSine and cosineAdjunctionMonadNatural TransformationYoneda LemmaRandom variable
Relationship types

172 concepts viewed through this lens. Bridge concepts connect this view to Acoustics, Actuarial Science, Agriculture, Algorithms….

Legend
  • Focused concept
  • Connected concept
  • Bridge concept (just outside the lens)
  • Arrow points from cause / source to effect / target
  • A line with no arrow is a two-way relationship
  • Node colour marks the concept’s primary discipline
22 concepts22 relationships9 disciplines5 relation families

At a glance

A morphism is a structure-preserving arrow from one object to another; composing morphisms is the heart of category theory.

Disciplines
Category Theory · Mathematics
Role in the graph
Cross-disciplinary bridge — reaches Algebra, Set Theory
Relationships
4 · 2 relation families

What am I looking at?

In this lens (172)

Bridge concepts (186)

Just outside the lens — they connect it to other context.

  • Rate of change5
    Calculus, Economics, Physics · connects to Differential equation, Integral, Limit…
  • Enumerative counting4
    Combinatorics · connects to Combination, Generating function, Permutation…
  • Graph data structure4
    Computer Science, Data Structures · connects to Connectivity, Edge, Shortest path…
  • Machine learning3
    Artificial Intelligence, Computer Science, Machine Learning, Statistics · connects to Algorithm, Pattern, Probability
  • Optimization3
    Business, Economics, Engineering, Mathematical Modelling, Optimization, Systems Engineering · connects to Inequality, Linear programming, Mathematical model

Insights from this view

Structural observations about the concepts shown here — descriptions of this graph, not claims about the world.

  • This view connects 9 disciplines: Algebra, Calculus, Category Theory, Discrete Mathematics, Geometry, Logic, Mathematics, Probability, Set Theory.
  • Morphism is a bridge concept — viewed here through Category Theory, Mathematics.
  • The connections here span 5 relation families.

Relationships as a list

The focused concept’s relationships. Pick another concept in the graph above to update this list.

Explore through a different lens

A lens is a deterministic projection of the graph. Pick a discipline, thinking pattern or journey to reframe the whole view.

By discipline

ChemistryBiologyPhysicsMathematicsComputer ScienceGeologyMineralogyEconomics

By thinking pattern

Bayesian updatingCause and effectCompoundingConservationConstraintsDefense in depthDiffusion & spreadEmergenceEnergy transformationEntropy & irreversibilityEquilibriumFeedback loopIncentivesInformationLevels & hierarchyModularityNetworksOptimizationOscillationProbabilityRecursion & self-similarityScaleSignal vs noiseSource–pathway–receptorStocks and flowsSymmetry & invarianceThresholds & tipping pointsTrade-offsTriangulationVariation & selectionWaves

By journey

From a Leaf to the ClimateWhy Music Moves UsHow Machines LearnReasoning about a Leaf and the Climate

Concept collections

Concept collections are curated lenses onto the fabric — themed sets of ideas that recur across disciplines. They are not journeys; they are a way to read the graph.

About this view

What this is

Start from one concept and expand outward. The view never shows everything at once — click a node to refocus, filter by relationship type, or switch to an accessible list.

One fabric

3750 concepts and 5051 typed relations form one connected component — no isolated silo.

How to read it

Focus a concept, or apply a lens (discipline, mental model, journey) to see only the threads that matter.