Towards free localic algebras

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003 Unisa, South Africa. National Institute for Theoretical and Computational Sciences (NITheCS), South Africa.

10.48308/cgasa.2024.233933.1445

Abstract

The purpose of this paper is to establish that the underlying object
functor from the models of a Lawvere theory to the base category creates limits
and coequalisers of all parallel pairs of homomorphisms whose underlying pair
admit a split coequaliser. We show that for a small complete category with
a well behaved proper factorisation structure, the underlying functor admits
a left adjoint and the category of such models is precisely monadic over the
base category in the sense of Beck’s Theorem. In particular, this establishes
the existence of free localic algebras for any Lawvere theory, generalising the
known results for the existence of free localic groups.

Keywords

Main Subjects

References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 26 August 2024

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