1. Completing Categorical Algebras
- Author
-
Zoltán Ésik and Stephen L. Bloom
- Subjects
Set (abstract data type) ,Combinatorics ,Functor ,Mathematics::Category Theory ,Natural transformation ,Ordered set ,Mathematics::Algebraic Topology ,Categorical variable ,Initial and terminal objects ,Mathematics - Abstract
Let Σ be a ranked set. A categorical Σ-algebra, cΣa for short, is a small category C equipped with a functor σC: C n →C, for each σ ∈ Σn, n ≥ 0. A continuous categorical Σ-algebra is a cΣa which has an initial object and all colimits of ω-chains, i.e., functors ℕ≥C; each functor σc preserves colimits of ω-chains. (ℕ is the linearly ordered set of the nonnegative integers considered as a category as usual.)
- Published
- 2006