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#weighted — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #weighted, aggregated by home.social.

  1. #First we #reformulate #ordinary #colimits in the #language of #tensor #products, in a #way that #suggests #more #general #weighted colimits.

    #Assume for the #moment that the #receiving category C has all #coproducts and #coequalizers. As is #well #known, it #follows that C #has #all colimits; the #proof is we can #write #down a #formula for the colimit of F:J→C: as a #coequalizer of a #pair:

    ∑j,k∈Ob(J)hom(j,k)×F(j) [[→ →]] ∑k∈Ob(J)F(k) [[→]] colimJF