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Category Theory Explorer

Interactive 3D category theory diagram: place objects, draw morphisms between them, watch composite morphisms g∘f build automatically, and see a live functor mapping into a second category.

Mathematics3DAdvanced60 FPS

Details

CategoryMathematics

RenderingThree.js · WebGL

DifficultyAdvanced

Target FPS60

ControlsObject mode: click empty space in the main category zone to add a new object. Morphism mode: click two objects in order to draw a morphism f: A→B between them; composite morphisms g∘f are built and drawn automatically whenever a chain exists. Show composition button pulses the most recent composite arrow. Reset restores the 3-object demo category.

Three.jscategory theoryabstract algebrafunctormorphism composition

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Build a small category by hand: drop objects into 3D space, connect them with morphisms, and watch composite morphisms and a colour-matched functor image appear automatically as the structure grows.

⚙ Under the hood

Interactive 3D category-theory diagram: place objects as spheres, click two objects to draw a morphism between them, and watch composite morphisms g∘f build and highlight automatically when f: A→B and g: B→C both exist. A second, colour-matched mini category shows a live functor mapping.

Three.jscategory theoryabstract algebrafunctormorphism composition

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install