→ Category Theory

Izifundo

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.

Izifundo eziningi

Ezinye zalezi zifundo zithathwe emathebhu avulekile: Wikipedia. Ikhasi ngalinye lesifundo linikeza igama lomsuka nelayisense.

Amaphawu asetshenziswa lapha

Chofoza noma yiluphi uphawu lwesibonakaliso ukuze uthole ukuchaza okuphelele, isithombe, kanye nokuthi iyiphi inhlamvu ekhona ekhuluma ngaso.

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.

Imibuzo abantu bebuza

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.

∑ Utholakele izinkinga?
Bhala noma udwebe kukhasi lokulungisa: ngayinye inqubekela phambili, isithombe, impendulo ifihlakele kuze kube ubuza. Isinqumo →

Okunye

＋ 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