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
The wedge sum of two pointed sets and is the quotient set of the disjoint union where both copies of the basepoint (the one in and the one in ) are identified. The wedge sum can be identified with a subset of the cartesian product ; if this subset is collapsed to a point, then the result is the smash product .
The wedge sum can be generalised to pointed objects in any category with pushouts, and is the coproduct in the category of pointed objects in (which is the coslice category ). A very commonly used case is when Top is a category of topological spaces.
Also, the wedge sum also makes sense for any family of pointed objects, not just for two of them, as long as has pushouts of that size.
For a set of pointed objects in a category with colimits, their wedge sum is the pushout
A wedge sum of pointed circles is also called a bouquet of circles. See for instance at Nielsen-Schreier theorem.
For a CW complex with filtered topological space structure the quotient topological spaces are wedge sums of -spheres.
Revised on October 26, 2012 01:10:32
by Toby Bartels