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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 20th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexMoving the following old query out of the entry to here. Maybe it inspires somebody to add to the entry a remark towards the answer: *** [ begin forwarded query ] +-- {: .query} Anonymous: Under what conditions are all injections in a category monomorphisms? Obviously injections are monomorphisms in a [[well-pointed]] [[topos]] or [[pretopos]] (those are models of particular types of set theories), but does that remain true in a (pre)topos without well-pointedness, a [[coherent category]] or an [[exact category]]? Anonymous: There is [this stackexchange post](https://math.stackexchange.com/questions/53405/conditions-for-monic-iff-injective), but the answers only refer to concrete categories with a [[forgetful functor]] to Set and a [[free functor]] from Set, rather than arbitrary abstract categories. =-- [ end forwarded query ] <a href="https://ncatlab.org/nlab/revision/diff/injection/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/injection/19">v19</a>, <a href="https://ncatlab.org/nlab/show/injection">current</a>

   Moving the following old query out of the entry to here. Maybe it inspires somebody to add to the entry a remark towards the answer:

   ---

   [ begin forwarded query ]

   +– {: .query} Anonymous: Under what conditions are all injections in a category monomorphisms? Obviously injections are monomorphisms in a well-pointed topos or pretopos (those are models of particular types of set theories), but does that remain true in a (pre)topos without well-pointedness, a coherent category or an exact category?

   Anonymous: There is this stackexchange post, but the answers only refer to concrete categories with a forgetful functor to Set and a free functor from Set, rather than arbitrary abstract categories. =–

   [ end forwarded query ]

   diff, v19, current