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concrete category
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(Definition)
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A concrete category over a category
 is a category
 together with a faithful functor
 . (The functor  is sometimes called the forgetful functor or the underlying functor.)
A concrete category over
 is called a construct. (Here
 denotes the category of sets.)
This means that in a construct objects can be interpreted as sets and morphisms as maps.
- 1
- J. Adámek, H. Herrlich, and G. Strecker.
Abstract and Concrete Categories.
Wiley, New York, 1990.
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"concrete category" is owned by kompik. [ full author list (3) ]
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(view preamble)
| Also defines: |
forgetful functor, underlying functor |
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Cross-references: maps, morphisms, objects, category of sets, functor, faithful functor, category
There are 17 references to this entry.
This is version 6 of concrete category, born on 2006-06-30, modified 2007-06-16.
Object id is 8118, canonical name is ConcreteCategory.
Accessed 2100 times total.
Classification:
| AMS MSC: | 18A05 (Category theory; homological algebra :: General theory of categories and functors :: Definitions, generalizations) |
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Pending Errata and Addenda
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