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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 3rd 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/quotient+object+coclassifier/1">v1</a>, <a href="https://ncatlab.org/nlab/show/quotient+object+coclassifier">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 4th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexFixed the first sentence from > In a [[finitely cocomplete category]], the [[dual]] of a [[subobject classifier]]. to: > The notion of a *quotient object coclassifier* in a [[finitely cocomplete category]] is [[abstract duality|dual]] to that of a *[[subobject classifier]]* in a [[finitely complete category]]. and changed the link from *[[dual]]* to *[[abstract duality]]*. <a href="https://ncatlab.org/nlab/revision/diff/quotient+object+coclassifier/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/quotient+object+coclassifier/2">v2</a>, <a href="https://ncatlab.org/nlab/show/quotient+object+coclassifier">current</a>

   Fixed the first sentence from

   In a finitely cocomplete category, the dual of a subobject classifier.

   to:

   The notion of a quotient object coclassifier in a finitely cocomplete category is dual to that of a subobject classifier in a finitely complete category.

   and changed the link from dual to abstract duality.

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 4th 2022
   • (edited Jun 4th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso improved the typesetting of the commuting square, from: $$ \array{ Q &\stackrel{\epsilon}{\to}& \mathbb{0} \\ \downarrow^{\digamma_U} && \downarrow^{\exists !} \\ X &\stackrel{f}{\to}& U } $$ \array{ Q &\stackrel{\epsilon}{\to}& \mathbb{0} \\ \downarrow^{\digamma_U} && \downarrow^{\exists !} \\ X &\stackrel{f}{\to}& U } to: $$ \array{ Q &\overset{\epsilon}{\longrightarrow}& \mathbb{0} \\ \big\downarrow {}^{\mathrlap{\digamma_U}} && \big\downarrow {}^{\mathrlap{\exists !}} \\ X &\underset{f}{\longrightarrow}& U } $$ \array{ Q &\overset{\epsilon}{\longrightarrow}& \mathbb{0} \\ \big\downarrow {}^{\mathrlap{\digamma_U}} && \big\downarrow {}^{\mathrlap{\exists !}} \\ X &\underset{f}{\longrightarrow}& U } <a href="https://ncatlab.org/nlab/revision/diff/quotient+object+coclassifier/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/quotient+object+coclassifier/2">v2</a>, <a href="https://ncatlab.org/nlab/show/quotient+object+coclassifier">current</a>

   also improved the typesetting of the commuting square, from:

   $$\array{ Q &\stackrel{\epsilon}{\to}& \mathbb{0} \\ \downarrow^{\digamma_U} && \downarrow^{\exists !} \\ X &\stackrel{f}{\to}& U }$$

   \array{
     Q &\stackrel{\epsilon}{\to}& \mathbb{0}   
     \\
     \downarrow^{\digamma_U} && \downarrow^{\exists !}
     \\
     X &\stackrel{f}{\to}& U
   }
   

   to:

   $$\array{ Q &\overset{\epsilon}{\longrightarrow}& \mathbb{0} \\ \big\downarrow {}^{\mathrlap{\digamma_U}} && \big\downarrow {}^{\mathrlap{\exists !}} \\ X &\underset{f}{\longrightarrow}& U }$$

   \array{
     Q 
       &\overset{\epsilon}{\longrightarrow}& 
     \mathbb{0}   
     \\
     \big\downarrow {}^{\mathrlap{\digamma_U}} 
     && 
     \big\downarrow {}^{\mathrlap{\exists !}}
     \\
     X 
       &\underset{f}{\longrightarrow}& 
     U
   }
   

   diff, v2, current