nLab
union
Context
Limits and colimits
limits and colimits
1Categorical

limit and colimit

limits and colimits by example

commutativity of limits and colimits

small limit

filtered colimit

sifted colimit

connected limit, wide pullback

preserved limit, reflected limit, created limit

product, fiber product, base change, coproduct, pullback, pushout, cobase change, equalizer, coequalizer, join, meet, terminal object, initial object, direct product, direct sum

finite limit

Kan extension

weighted limit

end and coend
2Categorical
(∞,1)Categorical
Modelcategorical
Contents
Definition
A union is a join of subsets or (more generally) subobjects. This includes the traditional settheoretic 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 wellbehaved unions of subobjects.
Revised on May 29, 2012 22:04:00
by
Andrew Stacey
(129.241.15.200)