A new technical report available via DspaceUNM at https://repository.unm.edu/dspace/handle/1928/10424 and also on my website, http://www.ece.unm.edu/~mjhealy/, describes our initial work in applying category theory to the modeling of temporal sequences in neural memories. With our categorical neural semantic theory (CNST), we take an alternative to most current approaches dealing with temporal sequencing, for example in forming episodic memories. We model the buildup of temporal sequences as the adaptation of neural structures representing colimits from a concept category mapped to a neural category by a functor. A more advanced model would express diagrams of functors connected by natural transformations, discussed as a general modeling scheme in prior papers (also available on my website). We claim that this approach is of fundamental importance in understanding the semantics of neural architectures. The report: M. J. Healy and T. P. Caudell (2010) "Temporal Sequencing via Supertemplates", UNM Technical Report EECE-TR-10-0001, DspaceUNM, University of New Mexico. Abstract A category-theoretic account of neural network semantics has been used to characterize incremental concept representation in neural memory. It involves a category of concepts and concept morphisms together with categories of objects and morphisms representing the activity in connectionist structures at different stages of weight adaptation. Colimits express the more specialized concepts as combinations of abstract concepts along shared subconcept relationships specified in diagrams. This provides a mathematical model of concept blending, in which designated relationships among concepts are preserved in a combination. Structure-preserving mappings called functors from the concept to neural categories provide a mathematical model of incremental concept representation through stages of adaptation. The work reported here extends these ideas to express temporal sequences of events, such as episodic memories. This requires an extended notion of neural morphism and a design principle for diagrams involving concepts in a temporal sequence. This is tested in a new architecture that involves a notion of supertemplates, which are ART network templates extending over a multi-level ART hierarchy with an interposed temporal integrator network. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]