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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 22nd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something, to be another item of _[[internalization]]_ along with _[[monoid object]]_ and _[[group object]]_. Not done yet, but need to save. (Our entry "[[action]]" does cover internal notions of actions, but it seems hard to bring that old entry into a good shape, and in any case splitting off an entry on the internal notion might just be the first step of bringing it into shape) The evident question for compiling this entry is: What are the canonical original references? Eckmann-Hilton in their articles originally introducing the notion of internal group objects ([here](https://ncatlab.org/nlab/show/group+object#References)) have all the ingredients in hand to say "action object", but it seems they don't (?). I found the notion stated clearly and explicitly, albeit somewhat in passing, in: * [[Francis Borceux]], [[George Janelidze]], [[Gregory Maxwell Kelly]], p. 8 of: _Internal object actions_, Commentationes Mathematicae Universitatis Carolinae (2005) Volume: 46, Issue: 2, page 235-255 ([dml:249553](https://eudml.org/doc/249553)) but if anyone has other/better references, let's add them. <a href="https://ncatlab.org/nlab/revision/action+object/1">v1</a>, <a href="https://ncatlab.org/nlab/show/action+object">current</a>

   starting something, to be another item of internalization along with monoid object and group object.

   Not done yet, but need to save.

   (Our entry “action” does cover internal notions of actions, but it seems hard to bring that old entry into a good shape, and in any case splitting off an entry on the internal notion might just be the first step of bringing it into shape)

   The evident question for compiling this entry is: What are the canonical original references?

   Eckmann-Hilton in their articles originally introducing the notion of internal group objects (here) have all the ingredients in hand to say “action object”, but it seems they don’t (?).

   I found the notion stated clearly and explicitly, albeit somewhat in passing, in:

   • Francis Borceux, George Janelidze, Gregory Maxwell Kelly, p. 8 of: Internal object actions, Commentationes Mathematicae Universitatis Carolinae (2005) Volume: 46, Issue: 2, page 235-255 (dml:249553)

   but if anyone has other/better references, let’s add them.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 22nd 2021
   • (edited Mar 22nd 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexoh, darn, (only) now I remember that we have already _[[module object]]_. Am merging this with _[[action object]]_ now. Sorry for the noise here. But this shows we need a table _[[categorical algebra -- contents]]_. Will create one... <a href="https://ncatlab.org/nlab/revision/action+object+%3E+history/1">v1</a>, <a href="https://ncatlab.org/nlab/show/action+object+%3E+history">current</a>

   oh, darn, (only) now I remember that we have already module object. Am merging this with action object now.

   Sorry for the noise here. But this shows we need a table categorical algebra – contents. Will create one…

   v1, current