Higher Dimensional Algebra
نویسندگان
چکیده
منابع مشابه
Higher Dimensional Algebra Vii: Groupoidification
Groupoidification is a form of categorification in which vector spaces are replaced by groupoids and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed exposition of ‘degroupoidification’: a systematic process that turns groupoids and spans into vector spaces and linear operators. Then we present three applications of groupoidification. The first is to F...
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A 2-group is a ‘categorified’ version of a group, in which the underlying set G has been replaced by a category and the multiplication map m: G×G → G has been replaced by a functor. Various versions of this notion have already been explored; our goal here is to provide a detailed introduction to two, which we call ‘weak’ and ‘coherent’ 2-groups. A weak 2-group is a weak monoidal category in whi...
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Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...
متن کاملHigher-Dimensional Algebra and Planck-Scale Physics
This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a ‘background-free quantum theory with local degrees of freedom propagating causally’. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3-dimensio...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1996
ISSN: 0001-8708
DOI: 10.1006/aima.1996.0052