Group Homomorphism - The Category of Groups

The Category of Groups

If and are group homomorphisms, then so is . This shows that the class (in a sense of category theory) of all groups, together with group homomorphisms as morphisms, forms a category.

Read more about this topic:  Group Homomorphism

Famous quotes containing the words category and/or groups:

    “Despair is typical of those who do not understand the causes of evil, see no way out, and are incapable of struggle. The modern industrial proletariat does not belong to the category of such classes.”
    —Vladimir Ilyich Lenin (1870–1924)

    “Under weak government, in a wide, thinly populated country, in the struggle against the raw natural environment and with the free play of economic forces, unified social groups become the transmitters of culture.”
    —Johan Huizinga (1872–1945)