→ Category Theory

გაკვეთილებიComment

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.

მეტი გაკვეთილი

Some of these lessons are adapted from open texts: Wikipedia. ყველა სავარჯიშო გვერდი ასახელებს მის წყაროსა და ლიცენზიას.

აქ გამოყენებული სიმბოლოები

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.

Questions people ask

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.

∑ Have a problem of your own?
ჩაწერეთ ან დახაზეთ გადამწყვეტი გვერდზე: ყველა ნაბიჯი, სურათი, პასუხი დაცულია სანამ არ იკითხავთ. გადაჭრა →

სხვა კალათა

＋ 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