Towards free localic algebras | ||
| Categories and General Algebraic Structures with Applications | ||
| دوره 22، شماره 1، فروردین 2025، صفحه 113-137 اصل مقاله (640.81 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.48308/cgasa.2024.233933.1445 | ||
| نویسندگان | ||
| Nathan Mulaja Tshakatumba* 1؛ Partha Pratim Ghosh2؛ Inderasan Naidoo2 | ||
| 1Department 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. | ||
| 2Department 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. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Beck's Theorem؛ Freyd's Adjoint Functor Theorem؛ co-well-powered category؛ Lawvere theory؛ monadicity؛ nearly PTT | ||
| مراجع | ||
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