→ Category Theory

Waxbarasho

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.

Waxbarasho dheeraad ah

Qaar ka mid ah koorsooyinkan waxaa laga soo qaatay qoraalo furan: Wikipedia. Bog kasta oo waxbarasho ah wuxuu ku magacaabaa asalkiisa iyo liisankiisa.

Calaamadaha la isticmaalay halkan

Taab calaamad kasta oo loogu talagalay qeexidda buuxda, sawir, iyo waxa xarfaha oo dhan ka mid ah ka dhigan tahay.

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.

Su'aalaha dadku waydiiyaan

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.

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