categorías: en Herstein y otros encontramos…


CATEGORÍA

OBJETOS Y MORFISMOS

 \mathfrak{C}

{\rm {obj}}\mathfrak{C}, \hom{\mathfrak{C}} 

SET

Conjuntos y mapeos

GP

Grupos y homomorfismos

RING

Anillos y morfismos de anillos

FIELD

Campos y …

MOD

Módulos y …

EV

espacios vectoriales y transformaciones lineales

ALG

Álgebras …

sGP

Semigrupos …

MON

Monoides …

GPDE

Grupoides …

 

 

TOPO

Espacios topológicos y funciones continuas

BANACH

Espacios de Banach …

HILBERT

Espacios de Hilbert …

CHAIN COMPLEXES

Cadenas complejas y cadeno morfismos

 

Little more on categories at PlanetMath.org

 Universal algebra links in John Baez’s page

It is possible to relate two categories: A functor is a transformation

F:{\rm{CAT}}_1\to {\rm{CAT}}_2

which send objects in {\rm{CAT}}_1 to objects in {\rm{CAT}}_2 and if \xi :X_1\to X_2 is a morphism inter two objects X1,X_2\in{\rm{CAT}}_1 then

F(\xi):F(X1)\to F(X_2)

is a morphism \in{\rm{CAT}}_2. It is a common practice to mane {\rm{Hom}}(X,Y) to the set of morphisms among the objects X,Y in a category. Then a functor maps {\rm{Hom}}(X,Y)\to {\rm{Hom}}(FX,FY)

  • The simplest example is the forgetful one GP\to SET which gives to each group the underliying set, i.e. forgets the binary operation in the group
  • Other example of a Functor is: {\rm{Ab}}: GP\to GPA given by G\to G/[G,G], which is the “abelianization of the group”
  • Another: {\rm{TOPOAC}}\to {\rm{GP}} given by X\to \pi_1(X) the fundamental group functor, where TOPOAC is the category of arc-connected topo-spaces
  • Cohomology functor. {\rm{TOPOPAIRS}}\stackrel{H^*}\to {\rm{CHAINCOMPLEXES}} given by (X,A)\mapsto \{H^0(A)\to H^0(X)\to H^0(X,A)\to H^1(A)\to ...\} which assigns to each topo-pair its cohomology-long-exact-sequence

Category in EOM More Pro reference

 

more on cat here in WP

One response to “categorías: en Herstein y otros encontramos…

  1. juanmarqz

    Haben mein Freund, Sie auf die Namen für Kategorien verwiesen?
    Erzählen Sie mir, wenn Sie schon dem Begriff ein der Kategorie begegnet haben, mir erzählt der derjenig.
    Erschrecken Sie nicht und fühlen Sie Angriff auf meinen Fragen auf dieser Wechselwirkung bitte.
    Begrüßt

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