u-Singularity and t-Topos Theoretic Entropy

Goro C. Kato, California Polytechnic State University - San Luis Obispo

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Copyright © 2010 Springer. The original publication is available at http://dx.doi.org/10.1007/s10773-010-0380-8.

Abstract

We will give descriptions of u-singularities as we introduce the notion of t-topos theoretic entropies. The unifying methodology for a u-singularity is the universal mapping property of an inverse or direct limit. The qualitative, conceptual, and structural analyses of u-singularities are given in terms of inverse and direct limits of micro decompositions of a presheaf and coverings of an object in t-site in the theory of temporal topos.