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containing identities and closed under composition, the relation 'there exists a
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are defined in a similar way. These concepts generalize respectively those of
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Nicola
Gambino and Peter Schuster, Spatiality for formal topologies
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is a totally ordered class with the classical ordering of ordinals.
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Adámek, Jiří; Horst
Herrlich; George E. Strecker (1990).
114:. However, it is difficult to work with them as in the
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with at most one morphism from an object to another.
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79:. Then, it is convenient to use the language of
47:, it is possible to define a class relation on
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118:case because many constructions common in a
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171:is a preorder on the class of objects of
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125:Equivalently, a preordered class is a
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203:Abstract and Concrete Categories
16:Class equipped with a preorder
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155:is a class of morphisms of
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43:When dealing with a class
209:. John Wiley & Sons.
96:Partially ordered class
70:{\displaystyle \times }
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108:partially ordered set
100:totally ordered class
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112:totally ordered set
55:of the power class
90:is a class with a
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31:equipped with a
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21:mathematics
239:Set theory
228:Categories
191:References
178:The class
120:set theory
83:on a set.
39:Definition
81:relations
65:×
184:ordinals
146:category
139:Examples
133:category
92:preorder
53:subclass
33:preorder
182:of all
151:, when
144:In any
94:on it.
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207:(PDF)
116:small
51:as a
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211:ISBN
110:and
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