Papers › Completeness for categories of generalized automata
Completeness for categories of generalized automata
Guido Boccali, Andrea Laretto, Fosco Loregian, Stefano Luneia
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We present a slick proof of completeness and cocompleteness for categories of F-automata, where the span of maps E←E⊗I →O that usually defines a deterministic automaton of input I and output O in a monoidal category (𝒦,⊗) is replaced by a span E←F E →O for a generic endofunctor F : 𝒦→𝒦 of a generic category 𝒦: these automata exist in their `Mealy' and `Moore' version and form categories F-𝖬𝗅𝗒 and F-𝖬𝗋𝖾; such categories can be presented as strict 2-pullbacks in 𝖢𝖺𝗍 and whenever F is a left adjoint, both F-𝖬𝗅𝗒 and F-𝖬𝗋𝖾 admit all limits and colimits that 𝒦 admits. We mechanize some of of our main results using the proof assistant Agda and the library `agda-categories`.
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