|zpravodaj ČSKI - prosinec 2013 |
datum: 4.12.2013 v 14:00
název: Ordered universal algebra, algebraic theories and Morita theorems
přednášející: Matěj Dostál
místo konání: UI, 2.patro, místnost č.318
souhrn: Sometimes doing something leads to the same result as doing something different. We are going to observe this phenomenon in the field of ordered universal algebra. In our approach, ordered universal algebra studies algebras with an underlying poset instead of a set, and with monotone (order-preserving) operations.
Varieties, or classes of algebras that are definable by equations between terms, are replaced with classes definable by inequalities between terms. Forming a closure of a set of inequalities yields an algebraic theory. An interesting question arises: when do two different algebraic theories give rise to classes of algebras that are equivalent as categories? The result is known in classical universal algebra and generalizes the work of Kiiti Morita in module theory. We show that the result generalizes even to the world of ordered universal algebra.