The second talk of these sessions should cover main properties of presheaves of spaces as developed in [5.1]. Bydefinition, ifCis an∞-category, then the∞-categoryP(C)is defined asFun(Cop,N(Kan))whereKanis thesimplicial category of Kan complexes andNis the simplicial nerve functor. Using the techniques we have studied sofar, one can produce an∞-category equivalent toP(C)using left fibrations [188.8.131.52] and prove that limits and colimitsin presheaves can be computed objectwise [§5.1.2]. Moreover, we can prove Yoneda lemma [184.108.40.206] and show thatthe Yoneda embedding preserves small limits [220.127.116.11].Please state the universal property of presheaves [18.104.22.168], and sketch the proof if possible.
Dienstag, den 4. Juni 2019 um 11:15 Uhr, in INF 205, SR 3 Dienstag, den 4. Juni 2019 at 11:15, in INF 205, SR 3