Abstract:
Confusingly for the uninitiated, experts in weak infinite-dimensional
category theory make use of different definitions of an ∞-category, and
theorems in the ∞-categorical literature are often proven "analytically",
in reference to the combinatorial specifications of a particular model. In
this talk, we present a new point of view on the foundations of ∞-category
theory, which allows us to develop the basic theory of ∞-categories ---
adjunctions, limits and colimits, co/cartesian fibrations, and pointwise
Kan extensions --- "synthetically" starting from axioms that describe an ∞-
*cosmos*, the infinite-dimensional category in which ∞-categories live as
objects. We demonstrate that the theorems proven in this manner are
"model-independent", i.e., invariant under change of model. Moreover, there
is a formal language with the feature that any statement about ∞-categories
that is expressible in that language is also invariant under change of
model, regardless of whether it is proven through synthetic or analytic
techniques. This is joint work with Dominic Verity.
Angelegt am Wednesday, 14.04.2021 12:50 von N. N
Geändert am Tuesday, 04.05.2021 15:39 von Anja Böckenholt
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