Lax Algebras: A Scenic Approach
|Other Titles:||Laxe Algebren: Ein szenischer Zugang||Authors:||Schubert, Christoph||Supervisor:||Porst, Hans-Eberhard||1. Expert:||Porst, Hans-Eberhard||2. Expert:||Tholen, Walter||Abstract:||
Lax algebras provide a setting for the simultaneous study of a wide range of topological structures. We propose scenes as an axiomatic setting for the study of lax algebras.After collecting basic facts on order-enriched categories, we present various methods to construct (lax) extensions of functors. We define lax algebras in a scenic context and present various examples. Exactness properties of categories of lax algebras are discussed. Here, special emphasis is put on strict and costrict morphisms, which provide a generalization of proper and open maps of topological spaces. Using strict morphisms a notion of compactness for lax algebras is discussed. For this notion of compactness a general Tychonoff-type theorem is proved.
|Keywords:||Lax algebras, order-enriched category, topological category, scenes||Issue Date:||1-Dec-2006||URN:||urn:nbn:de:gbv:46-diss000106027||Institution:||Universität Bremen||Faculty:||FB3 Mathematik/Informatik|
|Appears in Collections:||Dissertationen|
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