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Categorification | | John C. Baez
; James Dolan
; | | Date: |
5 Feb 1998 | | Subject: | Quantum Algebra; Category Theory | math.QA math.CT | | Abstract: | Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in turn should satisfy certain equations of their own, called `coherence laws’. Iterating this process requires a theory of `n-categories’, algebraic structures having objects, morphisms between objects, 2-morphisms between morphisms and so on up to n-morphisms. After a brief introduction to n-categories and their relation to homotopy theory, we discuss algebraic structures that can be seen as iterated categorifications of the natural numbers and integers. These include tangle n-categories, cobordism n-categories, and the homotopy n-types of the loop spaces Omega^k S^k. We conclude by describing a definition of weak n-categories based on the theory of operads. | | Source: | arXiv, math.QA/9802029 | | Services: | Forum | Review | PDF | Favorites | |
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