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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 nlab noncommutative noncommutative-geometry number-theory object 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 $U$ for which $U \times U$ 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 $U \leftarrow U \rightarrow U$ 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 $U \times U$ 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 $U$ in a category $C$ is subterminal or preterminal if any two morphisms 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,

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.