Equivalent Categories
It is a natural question to ask: under which conditions can two categories be considered to be "essentially the same", in the sense that theorems about one category can readily be transformed into theorems about the other category? The major tool one employs to describe such a situation is called equivalence of categories, which is given by appropriate functors between two categories. Categorical equivalence has found numerous applications in mathematics.
Read more about this topic: Category Theory
Famous quotes containing the words equivalent and/or categories:
“The notion that one will not survive a particular catastrophe is, in general terms, a comfort since it is equivalent to abolishing the catastrophe.”
—Iris Murdoch (b. 1919)
“all the categories which we employ to describe conscious mental acts, such as ideas, purposes, resolutions, and so on, can be applied to ... these latent states.”
—Sigmund Freud (1856–1939)