Decomposable Functors and the Exponential Principle

✍ Scribed by Andreas Dress; Thomas Müller

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 477 KB
• Volume: 129
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1997.1648

✦ Synopsis

We develop a combinatorial theory for the operation of forming the logarithm of generating functions associated with covariant functors on the category of finite sets and bijective maps. This leads to a rather general and flexible exponential principle for labeled combinatorial structures. We also introduce the concept of a topos-like category, which turns out to be a convenient framework for the discussion of a wide range of applications a few of which are studied in detail.