Timothy Porter

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We associate to a Hausdorff space, X, a double groupoid, ρ 2 (X), the homotopy double groupoid of X. The construction is based on the geometric notion of thin square. Under the equivalence of categories between small 2-categories and double categories with connection given in [BM] the homotopy double groupoid corresponds to the homotopy 2-groupoid, G2(X),(More)
We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as potential yoga for dealing with processes and processes of processes. Introduction There does seem to be a problem in neuroscience in finding a language suitable for describing brain(More)
We give an interpretation of Yetter’s Invariant of manifoldsM in terms of the homotopy type of the function space TOP(M,B(G)), where G is a crossed module and B(G) is its classifying space. From this formulation, there follows that Yetter’s invariant depends only on the homotopy type of M , and the weak homotopy type of the crossed module G. We use this(More)
Homotopy Quantum Field Theories (HQFTs) were introduced by the second author to extend the ideas and methods of Topological Quantum Field Theories to closed d-manifolds endowed with extra structure in the form of homotopy classes of maps into a given ‘target’ space, B. For d = 1, classifications of HQFTs in terms of algebraic structures are known when B is(More)