ONT Re: Higher Order Categorical Logic
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Note 3
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| Example C1'. Any set can be viewed as a category: a small 'discrete'
| category. The objects are its elements and there are no arrows except
| the obligatory identity arrows.
|
| Example C2'. Any monoid can be viewed as a category. There is only
| one object, which may remain nameless, and the arrows of the monoid
| are its elements. In particular, the identity arrow is the unity
| element. Composition is the binary operation of the monoid.
|
| Example C3'. Any preordered set can be viewed as a category.
| The objects are its elements and, for any pair of objects (a, b),
| there is at most one arrow a -> b, exactly one when a =< b.
|
| L&S, pages 5-6.
|
| Lambek, J. & Scott, P.J.,
|'Introduction To Higher Order Categorical Logic',
| Cambridge University Press, Cambridge, UK, 1986.
|
| http://uk.cambridge.org/mathematics/catalogue/0521356539/
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