Abstract
A theory of spectra in the setting of a general 2-category C with zeros is presented. The development closely parallels that already available in the topological setting of based spaces but requires significant modifications due to the attenuated setting. For example, even the existence of a suspension functor is not assumed. However, if C does admit a suspension functor, then a stable 2-category for C can be constructed. In the topological setting, an application of the results is made to extend the notion of W-topology, where W is a based space, as studied in [5]. Accordingly, W-topology is defined, where W is a spectrum. In the construction of both the stable 2-category and the W-topology 2-category, essential usage is made of the full image factorization of an arbitrary 2-functor.
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