In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms: instead of simply relating objects of a category to one another, morphisms become objects in their own right. This notion was introduced in 1963 by F. W. Lawvere, although the technique did not become generally known until many years later. Today, it has become particularly important to mathematicians, because several important mathematical concepts can be treated as comma categories. There are also certain guarantees about the existence of limits and colimits in the context of comma categories. The name comes from the notation originally used by Lawvere, which involved the comma punctuation mark. Although standard notation has changed since the use of a comma as an operator is potentially confusing, and even Lawvere dislikes the uninformative term "comma category", the name persists.
Read more about Comma Category: Definition, Properties
Famous quotes containing the words comma and/or category:
“I didn’t have to think up so much as a comma or a semicolon; it was all given, straight from the celestial recording room. Weary, I would beg for a break, an intermission, time enough, let’s say, to go to the toilet or take a breath of fresh air on the balcony. Nothing doing!”
—Henry Miller (1891–1980)
“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)