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Congruence Lattices of Ideals in Categories and (Partial) Semigroups
This monograph presents a unified framework for determining the congruences on a number of monoids and categories of transformations,
diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain
normal subgroup lattices on top of each other to successively build congruence lattices of a chain of ideals. This is applied to several
specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions;
Brauer, Temperley–Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations
are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid
categories.
eBook
Planar Algebras in Braided Tensor Categories
We generalize Jones’ planar algebras by internalising the notion to a pivotal braided tensor category
Building on our previous work on categorified
traces, we prove that there is an equivalence of categories between anchored planar algebras in
eBook
How to bake pi : an edible exploration of the mathematics of mathematics
\"In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard.\"--Publisher description.
Book
Non-semisimple extended topological quantum field theories
We develop the general theory for the construction of
eBook
Cohomological Tensor Functors on Representations of the General Linear Supergroup
We define and study cohomological tensor functors from the category
eBook
Higher topos theory
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics.
eBook