Comma Category

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 CategoryDefinition, Properties

Other articles related to "comma category":

Comma Category - Examples of Use - Natural Transformations
... particular collection of morphisms of type of the form, while objects of the comma category contains all morphisms of type of such form ... A functor to the comma category selects that particular collection of morphisms ...

Famous quotes containing the words category and/or comma:

    I see no reason for calling my work poetry except that there is no other category in which to put it.
    Marianne Moore (1887–1972)

    From one casual of mine he picked this sentence. “After dinner, the men moved into the living room.” I explained to the professor that this was Ross’s way of giving the men time to push back their chairs and stand up. There must, as we know, be a comma after every move, made by men, on this earth.
    James Thurber (1894–1961)