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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorvarkor
   • CommentTimeFeb 21st 2024
   • PermaLink
   Author: varkor
   Format: MarkdownItexMention terminology "preterminal object". <a href="https://ncatlab.org/nlab/revision/diff/subterminal+object/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/subterminal+object/18">v18</a>, <a href="https://ncatlab.org/nlab/show/subterminal+object">current</a>

   Mention terminology “preterminal object”.

   diff, v18, current

2. • CommentRowNumber2.
   • CommentAuthorHurkyl
   • CommentTimeFeb 22nd 2024
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexChanged the wording of an equivalent statement, so that it doesn't leave open the possibility of a subterminal object $U$ for which $U \times U$ doesn't exist. <a href="https://ncatlab.org/nlab/revision/diff/subterminal+object/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/subterminal+object/19">v19</a>, <a href="https://ncatlab.org/nlab/show/subterminal+object">current</a>

   Changed the wording of an equivalent statement, so that it doesn’t leave open the possibility of a subterminal object for which doesn’t exist.

   diff, v19, current

3. • CommentRowNumber3.
   • CommentAuthormaxsnew
   • CommentTimeFeb 22nd 2024
   • PermaLink
   Author: maxsnew
   Format: MarkdownItexWhy not just say that the cone $U \leftarrow U \rightarrow U$ given by identities is a product?

   Why not just say that the cone given by identities is a product?

4. • CommentRowNumber4.
   • CommentAuthorHurkyl
   • CommentTimeFeb 22nd 2024
   • (edited Feb 22nd 2024)
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexI was just making an (IMO) minimal adjustment to the existing language. I don't really know what precisely the original wording wanted to emphasize. I just wanted to reword it to forestall any reactions wondering about $U \times U$ not existing that might slow a reader down.

   I was just making an (IMO) minimal adjustment to the existing language. I don’t really know what precisely the original wording wanted to emphasize. I just wanted to reword it to forestall any reactions wondering about not existing that might slow a reader down.

5. • CommentRowNumber5.
   • CommentAuthormaxsnew
   • CommentTimeFeb 22nd 2024
   • PermaLink
   Author: maxsnew
   Format: MarkdownItexAnother rewording of the product condition <a href="https://ncatlab.org/nlab/revision/diff/subterminal+object/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/subterminal+object/20">v20</a>, <a href="https://ncatlab.org/nlab/show/subterminal+object">current</a>

   Another rewording of the product condition

   diff, v20, current

6. • CommentRowNumber6.
   • CommentAuthorRodMcGuire
   • CommentTimeFeb 22nd 2024
   • PermaLink
   Author: RodMcGuire
   Format: MarkdownItexumm > An [[object]] $U$ in a [[category]] $C$ is **subterminal** or **preterminal** if any two [[morphism]]s with [[target]] $U$ and the same source are equal. In other words, $U$ is subterminal if for any object $X$, there is at most one morphism $X\to U$. > If C has a terminal object 1, then U is subterminal precisely if the unique morphism U→1 is monic, so that U represents a subobject of 1; hence the name “sub-terminal.” like anything associated with limits while the objects are unique the morphisms from or to them are not equal or unique but only unique up to isomorphism,

   umm

   An object in a category is subterminal or preterminal if any two morphisms with target and the same source are equal. In other words, is subterminal if for any object , there is at most one morphism .

   If C has a terminal object 1, then U is subterminal precisely if the unique morphism U→1 is monic, so that U represents a subobject of 1; hence the name “sub-terminal.”

   like anything associated with limits while the objects are unique the morphisms from or to them are not equal or unique but only unique up to isomorphism,

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeFeb 22nd 2024
   • (edited Feb 22nd 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexRe #6: The quoted text looks correct. The sentence after the quote seems to have the roles of objects and morphisms mixed up.

   Re #6: The quoted text looks correct. The sentence after the quote seems to have the roles of objects and morphisms mixed up.