Ruprecht-Karls-Universität Heidelberg
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„Sessions 6-7. Presheaves; definition, Yoneda embedding, the universal property.“
Prof. Dr. Alexander Schmidt, Universität Heidelberg

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 [5.1.1.1] and prove that limits and colimitsin presheaves can be computed objectwise [§5.1.2]. Moreover, we can prove Yoneda lemma [5.1.3.1] and show thatthe Yoneda embedding preserves small limits [5.1.3.2].Please state the universal property of presheaves [5.1.5.6], 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