limit and colimit

  1. limit (of a graph in category C)-final object of the cone category (w.r.t. the graph)-gluing (graph as well)
    eg. pullback; topological product
  2. colimit/direct limit-initial object of the cocone category-restriction
    eg. disjoint union; wedge product; stalk is the colimit of presheaf; for locale, the finite intersection reserves the colimit/arbitrary union; pushout
    so they both have universal property.