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
In universal algebra, a direct product is simply a product in a concrete category that is created by the forgetful functor.
Compare the direct sum, a more complicated concept.
Trivially, a cartesian product of sets is a direct product in Set.
One of the requirements of a topological category is that any family of objects must have a direct product, although the term ‘direct product’ is not used in topology.
Many algebraic categories, such as Grp, Ab, Ring, etc, also have all direct products; this is where the term ‘direct product’ originated.
The category of (-valued) models of any Lawvere theory has all direct products; this includes the examples from algebra above.
Revised on August 26, 2012 23:54:41
by Urs Schreiber