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:
“The truth is, no matter how trying they become, babies two and under don’t have the ability to make moral choices, so they can’t be “bad.” That category only exists in the adult mind.”
—Anne Cassidy (20th century)
“Belonging to a group can provide the child with a variety of resources that an individual friendship often cannot—a sense of collective participation, experience with organizational roles, and group support in the enterprise of growing up. Groups also pose for the child some of the most acute problems of social life—of inclusion and exclusion, conformity and independence.”
—Zick Rubin (20th century)