Small and Large Categories
A category C is called small if both ob(C) and hom(C) are actually sets and not proper classes, and large otherwise. A locally small category is a category such that for all objects a and b, the hom-class hom(a, b) is a set, called a homset. Many important categories in mathematics (such as the category of sets), although not small, are at least locally small.
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And a small and a feeble populace stooping with mattock and spade,
Or weeding or ploughing with faces a-shining with much-toil wet;
While in this place and that place, with bodies unglorious, their chieftains stood....”
—William Butler Yeats (1865–1939)
“Where no great fish venture
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—Hilda Doolittle (1886–1961)
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—Gertrude Stein (1874–1946)
“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)