# Reflecting Algebraically Compact Functors

arXiv: https://arxiv.org/abs/1906.09649 · HTML: https://mlsanity.com/paper/1906.09649/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2019.

## Built on by (most cited first, 1 of 1)

- [Fibrational Initial Algebra-Final Coalgebra Coincidence over Initial Algebras: Turning Verification Witnesses Upside Down](https://mlsanity.com/paper/2105.04817/) (2021)

## Abstract (arXiv)

A compact T-algebra is an initial T-algebra whose inverse is a final T-coalgebra. 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 mixed-variance functors, such as function space. The construction of compact algebras is usually done in categories with a zero object where some form of a limit-colimit 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) limit-colimit 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.