Related papers: An informal introduction to topos theory
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.
We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…
This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely stroll through two themes (functorial semantics and…
These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differs slightly from…
In order to provide a good categorical setting to the many different spaces of fields arising in the description of physical theories, a pedagogical introduction to the categorical notion of smooth sets is provided and some simple…
We give an informal introduction to model categories, and treat three important examples in some details: the category of small categories, the category of dg algebras, and the category of small dg categories.
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…
We introduce some classes of genuine higher categories in homotopy type theory, defined as well-behaved subcategories of the category of types. We give several examples, and some techniques for showing other things are not examples. While…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
These notes give a brief introduction to the category of spectra as defined in stable homotopy theory. In particular, Section 5 discusses an extensive list of examples of spectra whose properties have been found to be interesting.
This is an introduction to Homotopy Type Theory and Univalent Foundations for philosophers, written as a chapter for the book "Categories for the Working Philosopher" (ed. Elaine Landry)
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
The paper is a naive introduction to descriptive set theory. It is aimed mathematicians without a background in logic. The goal is to provide the basic facts used for applications of descriptive set theory to other areas of mathematics,…
This expository article introduces the topic of roots in a compact Lie group. Compared to the many other treatments of this standard topic, I intended for mine to be relatively elementary, example-driven, and free of unnecessary…
We prove that every categorical model of dependent type theory with dependent sums and products, intensional identity types and univalent universes presents via its $\infty$-localisation an elementary $\infty$-topos, that is, a finitely…
This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.
The structure of almost topological space is a variation of the concept of topological space. It emerged as a formalization of a quantifier first order not definable from the usual existential and universal operators, named the quantifier…
These short lecture notes provide an introduction to some basic notions of F-theory with some special emphasis on its relation to Type IIB orientifolds with O7/O3-planes.
The classifying topos of a geometric theory is a topos such that geometric morphisms into it correspond to models of that theory. We study classifying toposes for different infinitary logics: first-order, sub-first-order (i.e. geometric…