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The set of morphisms (order-preserving functions) between two preorders actually has more structure than that of a set. It can be made into a preordered set itself by the pointwise relation:
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of two order-preserving functions is order preserving and the identity map is order preserving.
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is given by the same data as a 2-functor, but has the relaxed properties:
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This preordered set can in turn be considered as a category, which makes
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179:(considered as a preordered set) is the
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195:preordered sets. There are thus no
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172:order-preserving functions.
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258:. This functor has a left
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324:F from a category
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191:are precisely the
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227:forgetful functor
220:cartesian product
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104:December 2009
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311:2-category
225:We have a
187:, and the
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193:singleton
177:empty set
170:injective
151:morphisms
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458:Category
430:See also
248:faithful
244:function
168:are the
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260:adjoint
218:on the
208:product
143:objects
88:scholar
52:removed
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436:FinOrd
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175:The
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