# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Go back to the page of Subsection 1.1.1.

Comment #32 by Daniel on

[Typo:] "... then the evaluation of $C^{\cdot}$ on the morphism $\delta_i$ determines a map ..."

Comment #33 by Daniel on

[Typo:] "Notation 1.1.1.7. For every nonnegative integer $n$ and every integer $i$ with $0 \leq i \leq n$, we let $\sigma^i : [n+1] \to [n]$ denote the function given by the formula ..."

Comment #34 by Daniel on

[Typo:] "Remark 1.1.1.10. ... we have canonical bijections $(\operatorname{lim}_{C \in \mathcal{C}} S_{\cdot}(C))_n \simeq \operatorname{lim}_{C \in \mathcal{C}} (S_n(C))$."

Comment #44 by Kerodon on

Yep; thanks for these!

Comment #54 by Robert on

There is an extra parenthesis in the second equation, right after the $n$:

Comment #95 by Eugene on

Notation 1.1.1.1 seem to exclude $$. Am I missing something?

Comment #97 by Kerodon on

Whoops. Yes, the scope of the definition should include .

Comment #269 by Dominic Fox on

It's not clear to me whether Δ should include , since it is said to be equivalent to the category of non-empty finite linearly-ordered sets, and  is presumably empty.

Comment #270 by John Boger on

OK, I like the idea of a new foundation for mathematics -- I'd found set theory to be a bit lacking as a basis -- but now I'm completely lost from the word go. Can someone recommend prerequisite reading on category theory? I'm not even sure I fully understand what a "category"' means generally in mathematics, let alone thse infinity categories, and I certainly don't understand some of the other terms being used.

Comment #271 by Kerodon on

 denotes the set {0}, which has one element.

Comment #1348 by David Karapetyan on

"Can someone recommend prerequisite reading on category theory?"

There are several books for beginners. The ones I like are https://www.goodreads.com/book/show/2047855.Category_Theory and https://www.goodreads.com/book/show/22108484-basic-category-theory.

There are also:

• 12 comment(s) on Chapter 1: The Language of $\infty$-Categories
• 7 comment(s) on Section 1.1: Simplicial Sets

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