2,055 research outputs found
Categorical Abstract Rewriting Systems and Functoriality of Graph Transformation
Rewriting systems are often defined as binary relations over a given set of
objects. This simple definition is used to describe various properties of
rewriting such as termination, confluence, normal forms etc. In this paper, we
introduce a new notion of abstract rewriting in the framework of categories.
Then, we define the functoriality property of rewriting systems. This property
is sometimes called vertical composition. We show that most of graph
transformation systems are functorial and provide a counter-example of graph
transformation systems which is not functorial
Sullivan minimal models of operad algebras
preprintWe prove the existence of Sullivan minimal models of operad algebras, for a quite wide family of operads in the category of complexes of vector spaces over a field of characteristic zero. Our construction is an adaptation of Sullivan’s original step by step construction to the setting of operad algebras. The family of operads that we consider includes all operads concentrated in degree 0 as well as their minimal models. In particular, this gives Sullivan minimal models for algebras over Com, Ass and Lie, as well as over their minimal models Com8, Ass8 and Lie8. Other interesting operads, such as the operad Ger encoding Gerstenhaber algebras, also fit in our study.Preprin
- …