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Homotopy And Simple Homotopy Theory The ultimate sales letter will provide you a distinctive book to overcome you life to much greater. Book, as one of the reference to get many sources can be considered as one that will connect the life to the experience to the knowledge. By having book to read, you have tried to connect your life to be better. It will… (More)

- RONALD BROWN, KEITH A. HARDIE, +5 authors Timothy Porter
- 2002

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)

- A. Mutlu, Timothy Porter
- Applied Categorical Structures
- 2001

We introduce a pairing structure within the Moore complex NG of a simplicial group G and use it to investigate generators for NGn∩Dn where Dn is the subgroup generated by degenerate elements. This is applied to the study of algebraic models for homotopy types. A. M. S. Classification: 18D35 18G30 18G50 18G55.

- JOÃO FARIA MARTINS, TIMOTHY PORTER, Ronnie Brown, Gustavo Granja, Roger Picken, Marco Mackaay
- 2007

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)

- Timothy Porter
- 1996

We use presentations and identities among relations to give a generalisation of the Schreier theory of nonabelian extensions of groups. This replaces the usual multiplication table for the extension group by more efficient, and often geometric, data. The methods utilise crossed modules and crossed resolutions.

The aim is to explain and explore some of the current ideas from category theory that enable various mathematical descriptions of hierarchical structures.

- Timothy Porter, Vladimir Turaev
- 2007

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)

- Jean-Marc Cordier, Timothy Porter
- Applied Categorical Structures
- 1996

- Timothy Porter
- 2005

Simplicial formal maps were introduced in the first paper of this series as a tool for studying Homotopy Quantum Field Theories with background a general homotopy 2-type. Here we continue their study, showing how a natural generalisation can handle much more general backgrounds. The question of the geometric interpretation of these formal maps is partially… (More)