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The existence of the category of globular CW-complexes was already conjectured in [ 11 ].

ANR CATHRE — Categories, Homotopy and Rewriting

After localizing the category of globular CW-complexes by spatial and temporal deformations, we get a category the category of dihomotopy types whose objects up to isomorphism represent exactly the higher dimensional automata up to deformation. Thus globular CW-complexes provide a rigorous mathematical foundation to study from an algebraic topology point of view higher dimensional automata and concurrent computations.

Source Homology Homotopy Appl. Zentralblatt MATH identifier Gaucher, Philippe; Goubault, Eric. Topological deformation of higher dimensional automata.

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Higher-dimensional category

Online Price 1 Label: List. Online Price 1: Print Price 1 Label: List. Print Price 1: Online Price 2: Print Price 2: Online Price 3: Print Price 3: The opetopic definition of n -category has two stages.

Models, Logics, and Higher-Dimensional Categories: A Tribute to the Work of Mihaly Makkai

First, the language for describing k -cells is set up; this, in the language of Baez and Dolan, is the theory of opetopes. Then, a concept of universality is introduced, to deal with composition and coherence.

We first exhibit an equivalence between the three theories of opetopes as far as they have been proposed. We then give an explicit description of the category Opetope of opetopes.