Reflecting Algebraically Compact Functors
Abstract
A compact Talgebra is an initial Talgebra whose inverse is a final Tcoalgebra. Functors with this property are said to be algebraically compact. This is a very strong property used in programming semantics which allows one to interpret recursive datatypes involving mixedvariance functors, such as function space. The construction of compact algebras is usually done in categories with a zero object where some form of a limitcolimit coincidence exists. In this paper we consider a more abstract approach and show how one can construct compact algebras in categories which have neither a zero object, nor a (standard) limitcolimit coincidence by reflecting the compact algebras from categories which have both. In doing so, we provide a constructive description of a large class of algebraically compact functors (satisfying a compositionality principle) and show our methods compare quite favorably to other approaches from the literature.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.09649
 Bibcode:
 2019arXiv190609649Z
 Keywords:

 Computer Science  Logic in Computer Science;
 Mathematics  Category Theory
 EPrint:
 To appear in ACT'19 (Applied Category Theory conference)