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C-linear categories, simplicity and semisimplicity
Introducing C-linear categories, whose hom-sets are finite-dimensional complex vector spaces. The extra linear structure lets us define direct sums and leads naturally to the notions of simple objects and semisimplicity.
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Pivotal and ribbon categories
The notion of pivotal categories, for which the double dual of an object is equivalent to the object itself, and the concept of ribbon categories, where morphism equalities correspond to isotopies of ribbons in 3D space.
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Dual objects in category theory
Dual objects and dualizability, capturing the notion of maximally entangled states in categorical quantum mechanics. In the graphical calculus, this enables wires to bend backwards in time.
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Reconstructing linear algebra from categories
Notes on the linear structure of monoidal categories, following Heunen and Vicary's Categories for Quantum Theory, chapter 2.
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Monoidal category theory: An introduction to diagrams
Monoidal categories and their description in terms of string diagrams. Equations are correct if their diagrammatic representation holds up to planar (2D) isotopy — or spatial (3D) isotopy in braided monoidal categories.
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Basic notions of category theory, and what's to come
A basic introduction to categories: objects, morphisms, functors, equivalences, natural transformations, and universal properties.
Physics for Rainy Days