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Tao Gu (Jun 09 2021 at 16:08):We have a functor between two freely generated symmetric monoidal categories such that the image of generating objects in the source category are always generating objects in the target category. Is there a name/terminology for such functors? Or, is 'generator-preserving' an understandable name?
Matteo Capucci (he/him) (Jun 09 2021 at 16:26):Aren't these the images (under the free functor) of maps between generators themselves?
John Baez (Jun 09 2021 at 16:32):Sounds like a clear term to me. I don't know a standard term.
Amar Hadzihasanovic (Jun 09 2021 at 19:08):Morally speaking I would call them “cellular”, but “generator-preserving” is probably clearer for most audiences :)
Fabrizio Genovese (Jun 09 2021 at 21:36):Tao Gu said:
We have a functor between two freely generated symmetric monoidal categories such that the image of generating objects in the source category are always generating objects in the target category. Is there a name/terminology for such functors? Or, is 'generator-preserving' an understandable name?
In the Petri net literature, where these things are widely used, these are called "transition-preserving"
Fabrizio Genovese (Jun 09 2021 at 21:36):In the case of pre-nets it's exactly what you want. In the case of Petri net, each generator can be pre- and post- composed with a symmetry
Fabrizio Genovese (Jun 09 2021 at 21:37):But if you aren't doing Petri-nets this naming convention may look weird.