First presenter Co-presenter(s)
Name : Prof Pierre Bouchard * Name:   
E-mail: E-mail:  
Affiliation: University of Quebec at Montreal (UQAM) Name:   
Department: Mathematics  E-mail:    
City: Name:   
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Country: Canada Name:   
08-04  E-mail:    
Session: 8- Analogy in Reasoning and Construction Schedule:
Saturday, 9:15
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Title of
The Chemistry of Modern Combinatorics --
Category theory is a flourishing branch of mathematics that has the exploration of analogy as one of its major uses. I will give a very brief and naive introduction to the concepts of "category" and "functor". Then I will give simple definitions of a "species of structure F" and a "structure of species F over a finite set U", illustrated by numerous examples. I will then show what a "molecular" species is, give all examples of molecular species on a small number of elements, and use an example to show how every species can be decomposed into a "sum" of molecular species. From there I will show how to count the number of molecular species that there can be on a given finite set of n elements, and what two chemists found about that in 1929. To conclude, I will mention what an atomic species is, and show how any molecular species can be decomposed into a "product" of atomic species. Where can we go from there? The answer during the talk!