Content deleted Content added
m Signing comment by 178.197.234.69 - "→Shall we not avoid to talk about "Category of semi-groups" or "Category of non-empty Sets": new section" |
|||
Line 22:
Because semi-groups do not have an identity element, I guess we should not call them "category of semigroups".
Shall we not call them "questionable category of semigroups" or something in that spirit? <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/178.197.234.69|178.197.234.69]] ([[User talk:178.197.234.69#top|talk]]) 14:12, 24 October 2016 (UTC)</small> <!--Autosigned by SineBot-->
:In the case of categories whose objects are sets or which have an underlying set, the identity arrow is the [[identity mapping]] from the object to itself. This is the case here. For example, in the category of non-empty sets, the objects are sets and the arrows are mappings from a set to another (or to the same) set. This has to not be confused with the category that can be associated to a specific monoid, which has only one object and whose arrows are the elements of the monoid. Contrarily to preceding examples the category associated to a monoid has only one identity element, while the category of sets (or of monoids) has many identity arrows (one for each set or monoid). [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 16:28, 24 October 2016 (UTC)
| |||