→ Category Theory

उपक्रम

Instead of asking what things are, ask how they map to each other. Category theory finds the same pattern (a product, a limit, an adjunction) recurring across every branch, and gives it one name.

अधिक उपक्रम

यातील काही शिकवणी खुल्या पाठ्यपुस्तकांमधून घेण्यात आल्या आहेत: Wikipedia. प्रत्येक खंडात त्या त्या विषयाचे वर्णन व त्या विषयातील संशोधन आहे.

येथे वापरलेले चिन्ह

Tap any symbol for the full definition, a picture, and what every letter in it means.

F: \mathcal{C} \to \mathcal{D}functor, natural transformation
A structure-preserving map between categories; a map between functors.\operatorname{Hom}(Aarrows from A to B, composition
The set of morphisms; do g then f.

लोक विचारतात ते प्रश्न

What is a functor?

A map between categories that sends objects to objects and arrows to arrows while respecting composition. Taking the fundamental group of a space is a functor from spaces to groups.

∑ तुझ्या स्वतःच्या समस्या आहेत का?
Type it or draw it on the solver page: every step, a picture, the answer hidden until you ask. सोडवा →

इतर शाखा

＋ Arithmetic𝑥 Algebra△ Geometry∿ Trigonometryƒ Precalculusσ Statistics & Probability⊢ Discrete Math & Logic∫ Calculus⊞ Linear Algebraℕ Number Theoryẏ Differential Equations∇ Multivariable Calculusε Real Analysis⋔ Combinatorics & Graph Theory∈ Set Theory & Logic𝔾 Abstract Algebra𝑃 Probability Theory≈ Numerical Methodsℂ Complex Analysis◎ Topologyμ Measure Theory‖·‖ Functional Analysisκ Differential Geometryπ₁ Algebraic Topology∂ Partial Differential Equations≋ Fluid Dynamics∞ Frontiers