Table of Contents

Some thoughts on the future of category theory.- What are locally generated categories?.- Some remarks on free monoids in a topos.- A generic sheaf representation for rings.- Normalization equivalence, kernel equivalence and affine categories.- Computing quotients of actions of a free category.- A long exact sequence in non-abelian cohomology.- Algebraically complete categories.- Order-enriched sketches for typed lambda calculi..- First steps in synthetic domain theory.- Precategories and Galois theory.- How algebraic is the change-of-base functor?.- Fixpoint and loop constructions as colimits.- Preframe presentations present.- Strong stacks and classifying spaces.- Trees in distributive categories.- A note on relations relative to a factorization system.- Algebras for the partial map classifier monad.- Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes.- Concretely functorial programming.- Weak products over a locally Hausdorff locale.- Categorical interpolation: Descent and the Beck-Chevalley condition without direct images.- An n-categorical pasting theorem.- Topos-theoretic approaches to modality.- Negative sets have Euler characteristic and dimension.- Modular categories.- Some constructive results related to compactness and the (strong) Hausdorff property for locales.- An introduction to Tannaka duality and quantum groups.

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