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Stream: learning: questions

Topic: generator-preserving functors


view this post on Zulip 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?

view this post on Zulip Matteo Capucci (he/him) (Jun 09 2021 at 16:26):

Aren't these the images (under the free functor) of maps between generators themselves?

view this post on Zulip John Baez (Jun 09 2021 at 16:32):

Sounds like a clear term to me. I don't know a standard term.

view this post on Zulip Amar Hadzihasanovic (Jun 09 2021 at 19:08):

Morally speaking I would call them “cellular”, but “generator-preserving” is probably clearer for most audiences :)

view this post on Zulip 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"

view this post on Zulip 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

view this post on Zulip Fabrizio Genovese (Jun 09 2021 at 21:37):

But if you aren't doing Petri-nets this naming convention may look weird.