Limits and colimits
limits and colimits
limit and colimit
limits and colimits by example
commutativity of limits and colimits
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
end and coend
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 May 29, 2012 22:04:00
by Andrew Stacey