2014/10/29 by Pinto, Darllan Conceição, Mariano, Hugo Luiz
#03G27 #18A15 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1410.8083
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra. The logics are the objects in our categories of logics; the morphisms are certain signature morphisms that are translations between logics (\citeAFLM1,\citeAFLM2,\citeAFLM3 \citeFC). Morphisms between algebraizable logics (\citeBP) are translations that preserves algebraizing pairs (\citeMaMe): they can be completely encoded by certain functors defined on the quasi-variety canonically associated to the algebraizable logics. This kind of results will be useful in the development of a categorial approach to the representation theory of general logics (\citeMaPi1, \citeMaPi2, \citeAJMP).