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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 14th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/prefunction/1">v1</a>, <a href="https://ncatlab.org/nlab/show/prefunction">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 15th 2022
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   Author: Urs
   Format: MarkdownItexI have hyperlinked a few more of the technical terms (eg. *[[categorical semantics]]* and *[[(infinity,1)-category|$(\infty,1)$-category]]*). But I have also slightly touched wording and punctuation in a couple of paragraphs, in an attempt to make the text flow more easily. Please check if you agree: I have touched this paragraph: > In many [[foundations of mathematics|foundations]] based on [[type theory]], such as in [[Martin-Löf type theory]], all [[types]] come equipped with an [[identity type]] which behaves similarly as [[equality]] does in [[Sets|sets]]. These types, therefore, are not [[presets]] in the strict sense, in that the latter do not carry any equality at all. However, [[function type|functions]] between such types usually do not satisfy [[function extensionality]], so that in the set-theoretic sense they are still like prefunctions. and this one: > The difference between functions and prefunctions in sets is modeled in [[category theory]] ([[categorical semantics]]) as the difference between an [[evaluational category]] (a [[concrete category]] where [[morphisms]] behave as functions do in [[Set]]) and an [[extensional category]] (which is an evaluational category where all functions preserve the equality in sets) relating equality of elements to equality of functions. <a href="https://ncatlab.org/nlab/revision/diff/prefunction/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/prefunction/2">v2</a>, <a href="https://ncatlab.org/nlab/show/prefunction">current</a>

   I have hyperlinked a few more of the technical terms (eg. categorical semantics and $(\infty,1)$-category).

   But I have also slightly touched wording and punctuation in a couple of paragraphs, in an attempt to make the text flow more easily. Please check if you agree:

   I have touched this paragraph:

   In many foundations based on type theory, such as in Martin-Löf type theory, all types come equipped with an identity type which behaves similarly as equality does in sets. These types, therefore, are not presets in the strict sense, in that the latter do not carry any equality at all. However, functions between such types usually do not satisfy function extensionality, so that in the set-theoretic sense they are still like prefunctions.

   and this one:

   The difference between functions and prefunctions in sets is modeled in category theory (categorical semantics) as the difference between an evaluational category (a concrete category where morphisms behave as functions do in Set) and an extensional category (which is an evaluational category where all functions preserve the equality in sets) relating equality of elements to equality of functions.

   diff, v2, current