Directory UMM :Journals:Journal_of_mathematics:TAC:
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Before treating the general case of enriching over the k -fold monoidal category of enriched n -categories we examine the definition in the two lowest categorical dimensions.. This
The fibrant functors are precisely the pointwise fibrant functors which preserve weak equivalences, thus any enriched functor is weakly equivalent in the homotopy functor model
in [Baues & Jibladze 2002] it was proved that linear track extensions are essentially the same as groupoid enriched categories such that automorphism groups of all 1-arrows
d - Space of d-spaces (in the sense of [11]) is topological and its full subcategory generated by suitably ordered cubes is our proposed convenient category for directed homotopy..
By Theorem 2.4, for the class of strongly fibred spaces, shape and strong shape equivalences coincide, so that, in such a case homotopy orthogonality implies enriched
The notion of leaf-to-leaf transforming homotopic mappings is introduced, and the homotopy axiom for vertical cohomologies is proved (Theorem 2.5).. The notion of a relative group
approaches to modelling intuitionistic logic lead to toposes and sheaf categories; cf. Study numeric systems inside Heyting valued models and the corresponding algebraic structures;
Section 3 deals with the categories of chain complexes (a stable case) and positive complexes (left h-stable); these homotopical categories have a homotopical homology,
