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Top Papers in Category theory

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Set theory for category theory

Questions of set-theoretic size play an essential role in category theory,
especially the distinction between sets and proper classes (or small sets and
large sets). There are many different ways to f

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Who needs category theory?

In mathematical applications, category theory remains a contentious issue,
with enthusiastic fans and a skeptical majority. In a muted form this split
applies to the authors of this note. When we lear

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Basic Category Theory

This short introduction to category theory is for readers with relatively little mathematical background. At its heart is the concept of a universal property, important throughout mathematics. After a

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Category Theory for Genetics

We introduce a categorical language in which it is possible to talk about DNA
sequencing, alignment methods, CRISPR, homologous recombination, haplotypes,
and genetic linkage. This language takes the

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Univalence of univalent morphisms

Univalence in Higher Category Theory

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A Brief Introduction to Category Theory

Category Theory for Programming

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Category Theory with Stratified Set Theory

This paper examines the category theory of stratified set theory (NF and KF).
We work out the properties of the relevant categories of sets, and introduce a
functorial analogue to Specker's T-operatio

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category theoretic theory of finite Ramsey theory

Finite Ramsey Theory through Category Theory

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Category Free Category Theory and Its Philosophical Implications

There exists a dispute in philosophy, going back at least to Leibniz, whether
is it possible to view the world as a network of relations and relations
between relations with the role of objects, betwe

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Proceedings Applied Category Theory 2019

Applied Category Theory is a new conference series. All papers are carefully
refereed, and the bar for acceptance is high. This 1st occurrence in this
format resulted in some 70 submitted papers and 1

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Fibrations in $\infty$-category theory

In this short expository note, we discuss, with plenty of examples, the
bestiary of fibrations in quasicategory theory. We underscore the simplicity
and clarity of the constructions these fibrations m

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On Self-Predicative Universals in Category Theory

1. This paper shows how the universals of category theory in mathematics
provide a model (in the Platonic Heaven of mathematics) for the
self-predicative strand of Plato's Theory of Forms as well as f

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Formalizing Agda's Category Theory

Proof-relevant Category Theory in Agda

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Category Theory in the Sciences: An Example-Based Approach

Category theory for scientists (Old version)

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Infinity category theory from scratch

We use the terms "$\infty$-categories" and "$\infty$-functors" to mean the
objects and morphisms in an "$\infty$-cosmos." Quasi-categories, Segal
categories, complete Segal spaces, naturally marked si

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Category Theory Using String Diagrams

In work of Fokkinga and Meertens a calculational approach to category theory
is developed. The scheme has many merits, but sacrifices useful type
information in the move to an equational style of reas

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Axiomatic Method and Category Theory

Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of
heigher homotopy theory exemplify a new way of axiomatic theory building, which
goes beyond the classical Hibert-style Axioma

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Category Theory in Machine Learning

Category Theory in Machine Learning

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What is Applied Category Theory?

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 them

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On $\infty$-cosmoi of bicategories

An $\infty$-cosmos is a setting in which to develop the formal category
theory of $(\infty,1)$-categories. In this paper, we explore a few atypical
examples of $\infty$-cosmoi whose objects are 2-cate

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