Thinking·OS

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Explore the knowledge graph

Morphism is part of Category. Activate to inspect this relation.Functor applies to 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.Functor applies to Category. Activate to inspect this relation.Natural Transformation depends on Functor. Activate to inspect this relation.Isomorphism is a Morphism. Activate to inspect this relation.Product and Coproduct is derived from Universal Property. Activate to inspect this relation.Limit and Colimit is a Product and Coproduct. Activate to inspect this relation.Limit and Colimit is derived from Universal Property. Activate to inspect this relation.Adjunction depends on Functor. Activate to inspect this relation.Adjunction requires Natural Transformation. Activate to inspect this relation.Monad is derived from Adjunction. Activate to inspect this relation.Monad is a Functor. Activate to inspect this relation.Yoneda Lemma applies to Functor. Activate to inspect this relation.Yoneda Lemma explains Universal Property. Activate to inspect this relation.Duality applies to Category. Activate to inspect this relation.Duality explains Product and Coproduct. Activate to inspect this relation.AdjunctionFunctorNatural TransformationMonadCategoryCategoryYoneda LemmaMorphismDualityUniversal PropertyFunctionIsomorphismProduct and CoproductLimit and Colimit
Relationship types
Legend
  • Focused concept
  • Connected concept
  • 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
14 concepts18 relationships4 disciplines5 relation families

At a glance

An adjunction is a pair of functors related by a natural bijection of morphisms, one left and one right adjoint.

Disciplines
Category Theory
Role in the graph
Connector
Relationships
3 · 1 relation families

Insights from this view

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

  • This view connects 4 disciplines: Algebra, Category Theory, Mathematics, Set Theory.
  • Category 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.