[Turkmath:6036] FGC-Higher Structures Seminars::Redi Haderi[Bilkent Univ.][March.28, 2023 at 17:00-Istanbul time]

[kazimilhan.ikeda]

Dear friends,

This week our speaker is Redi Haderi from Bilkent University.
The details of his talk are as follows:

Speaker: Redi Haderi (Bilkent University)
Date and time: March 28, 2023, Tuesday at 17:00 Istanbul local time

Title: A simplicial category for higher correspondences.
Abstract:
Correspondences between simplicial sets (and oo-categories) are
a generalization of the notion of profunctor between categories.
It is known that functors between categories are classified by lax
diagram of profunctors. We will present this fact from the lens of
double category theory.
Then, we will show how simplicial sets, simplicial maps and
correspondences are organized in a simplicial category (this is a
weak simplicial object in categories). A simplicial category may
be regarded as a 2-fold version of a simplicially enriched category,
and hence some ideas from double category theory apply. In particular
we formulate the fact that simplicial maps are classified by diagrams
of correspondences. As a corollary, we obtain a formulation of Lurie's
prediction that inner fibrations are classified by diagrams of
correspondences between oo-categories.

Reference: https://arxiv.org/abs/2005.11597


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Best Regards,
K. Ilhan Ikeda
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