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1. • CommentRowNumber1.
   • CommentAuthorBrian Pinsky
   • CommentTimeJan 3rd 2021
   • PermaLink
   Author: Brian Pinsky
   Format: MarkdownItexThese two related principals are not the only axioms with this name. A more set-theoretic "axiom of multiple choice" also exists (which, as far as I can tell, is unrelated to these axioms). I added the set theoretic axiom and gave some references where it is used this way. <a href="https://ncatlab.org/nlab/revision/diff/axiom+of+multiple+choice/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/axiom+of+multiple+choice/15">v15</a>, <a href="https://ncatlab.org/nlab/show/axiom+of+multiple+choice">current</a>

   These two related principals are not the only axioms with this name. A more set-theoretic “axiom of multiple choice” also exists (which, as far as I can tell, is unrelated to these axioms). I added the set theoretic axiom and gave some references where it is used this way.

   diff, v15, current

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeJan 3rd 2021
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexAgain, I think it's worth considering creating a separate page for this other notion you're referring to. See my earlier comment in the other thread.

   Again, I think it’s worth considering creating a separate page for this other notion you’re referring to. See my earlier comment in the other thread.

3. • CommentRowNumber3.
   • CommentAuthornLab edit announcer
   • CommentTimeJul 21st 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexremoving query box from article +--{: .query} [[Mike Shulman]]: Are the first two the same? If not, why are they given the same name? [[Peter LeFanu Lumsdaine]]: Yes, they are equivalent. For any $X$, given a collection family $\{D_c\}_{c \in C}$ including $X$, then the family $\{D_c\}_{(c \in C, f : D_c \twoheadrightarrow X)}$” is an inhabited collection family equipped with surjections to $X$. Conversely, given an inhabited collection family equipped with surjections to $X$, throwing $X$ into the family gives a collection family including $X$. =-- Anonymous <a href="https://ncatlab.org/nlab/revision/diff/axiom+of+multiple+choice/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/axiom+of+multiple+choice/19">v19</a>, <a href="https://ncatlab.org/nlab/show/axiom+of+multiple+choice">current</a>

   removing query box from article

   +–{: .query} Mike Shulman: Are the first two the same? If not, why are they given the same name?

   Peter LeFanu Lumsdaine: Yes, they are equivalent. For any $X$, given a collection family $\{D_c\}_{c \in C}$ including $X$, then the family $\{D_c\}_{(c \in C, f : D_c \twoheadrightarrow X)}$” is an inhabited collection family equipped with surjections to $X$. Conversely, given an inhabited collection family equipped with surjections to $X$, throwing $X$ into the family gives a collection family including $X$. =–

   Anonymous

   diff, v19, current