→ Category Theory

Kennslustund

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.

Fleiri kennslustundir

Sumir af þessum kennslustundum eru aðlagaðar frá opnum textum: Wikipedia. Hver kennslustundarsíða nefnir uppruna sinn og leyfi.

Tákn notuð hér

Pikkaðu á hvaða tákn sem er fyrir fulla skilgreiningu, mynd og hvað hvert bréf í því merkir.

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.

Spurningar sem fólk spyr

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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