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The Department this week
- Dalhousie introduces new Quality of Work Life survey
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- Sharing expertise with the world: New Dal MOOCs focus on obesity and youth mental health
- There's nothing boring about boron
- Introducing Dal's honorary degree recipients for Spring Convocation 2015
April 21, 2015 2:30 PM
Presented by - Richard Wood
Title - The interpolation lemma for the waves of a totally distributive category
Abstract - In a complete lattice, "Raney's anonymous relation", nowadays known as <<, is defined by k<<a iff, for all downsets S, a<=\/S implies k in S. Raney showed that if the complete lattice is completely distributive then k<<a implies, there exists m, with k<<m and m<<a. (He also remarked that << for the non-modular N_5 also satisfies this interpolative property, so that it does not characterize complete distibutivity.)
In this talk I will show that every wave \omega:K~~~>A in a totally distributive category factors as \psi \chi K~~~>M~~~>A and that the tensor \chi\ox\psi is uniquely determined. In passing from orders to categories, problems of both coherence and size occur. For example, we need to know what a composite \chi\circ\psi means to make sense of all this. The attached .pdf file for my proposed talk at CT15 provides some further context for this talk.