nLab
union
Context
Limits and colimits
limits and colimits
1-Categorical
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limit and colimit
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limits and colimits by example
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commutativity of limits and colimits
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filtered colimit
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sifted colimit
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preserved limit, reflected limit, created limit
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product, fiber product, base change, coproduct, pullback, pushout, cobase change, equalizer, coequalizer, join, meet, terminal object, initial object
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finite limit
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Kan extension
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weighted limit
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end and coend
2-Categorical
(∞,1)-Categorical
Model-categorical
Contents
Definition
A union is a join of subsets or (more generally) subobjects. This includes the traditional set-theoretic union of subsets of some ambient set.
The dual notion is that of intersection/meet.
Unions of completely arbitrary sets make sense only in material set theory, where their existence is guaranteed by the axiom of union. In structural set theory, unions of arbitrary sets can generally be replaced by disjoint unions.
A coherent category is one having well-behaved unions of subobjects.
Revised on January 5, 2012 20:02:38
by
Urs Schreiber
(89.204.138.119)