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 subquotient of an object in some category is
- a subobject of a quotient object of .
The two definitions are equivalent whenever quotients are stable under pullback and subobjects are stable under pushout, such as in a topos.
Just as with subobjects and quotient objects, we have that is a subquotient of itself, and subquotients of subquotients of are themselves subquotients of in a natural way.
Just as subobjects of a set are in correspondence with predicates on and quotients of are in correspondence with equivalence relations on , subquotients of are in correspondence with partial equivalence relations on .
Revised on January 1, 2011 09:33:03
by Urs Schreiber