Skip to search formSkip to main contentSkip to account menu
REVIEWS-Sketches of an elephant: A topos theory compendium
A1 Regular and Cartesian Closed Categories A2 Toposes - Basic Theory A3 Allegories A4 Geometric Morphisms - Basic Theory B1 Fibrations and Indexed Categories B2 Internal and Locally Internal…
Category Theory
Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer…
View via Publisher
Structure in Mathematics and Logic: A Categorical Perspective
View via Publisher
Homotopy theoretic models of identity types
  • S. Awodey, M. Warren
  • Mathematics
    Mathematical Proceedings of the Cambridge…
  • 3 September 2007
Quillen [17] introduced model categories as an abstract framework for homotopy theory which would apply to a wide range of mathematical settings. By all accounts this program has been a success…
View on Cambridge Press
An Answer to Hellman's Question: ‘Does Category Theory Provide a Framework for Mathematical Structuralism?’†
View via Publisher
Local realizability toposes and a modal logic for computability
TLDR
This work investigates a configuration of three toposes, which is regarded as describing a notion of relative computability, and deriving a modal calculus as its internal logic.
View on Cambridge Press
Carnap, Completeness, And Categoricity:The Gabelbarkeitssatz OF 1928
In 1929 Carnap gave a paper in Prague on “Investigations in General Axiomatics”; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult,…
View on Springer
Completeness and Categoricity. Part I: Nineteenth-century Axiomatics to Twentieth-century Metalogic
This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins…
View on Taylor & Francis
Natural models of homotopy type theory
  • S. Awodey
  • Mathematics
    Mathematical Structures in Computer Science
  • 12 June 2014
TLDR
It is shown that a category admits a natural model of type theory if it has a class of maps that behave like the abstract fibrations in axiomatic homotopy theory: They should be stable under pullback, closed under composition and relative products, and there should be weakly orthogonal factorizations into the class.
View on Cambridge Press
First-order logical duality
View PDF on arXiv
...
...
By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy Policy, Terms of Service, and Dataset License