cleaned up page and added a small ideas section too

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]]>removed homotopy groups of spheres results as they are already in homotopy groups of spheres (homotopytypetheory). I will need to add recent developments here too (such as Floris’ work).

]]>moved types here from type theory page.

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]]>I feel like this should be the analgoue of the first few chapters of the HoTT book for the HoTT wiki. The aim should be to list all type theoreticy things here, give the appropriate definitions and ideas with each article.

This will allow us to remark concretely in pages about say Synthetic homotopy theory about type theoretic results.

I have begun remodelling this page but I don’t really know what it will look like. I have made an effort to keep the old page in order to eventually incoroprate it.

]]>As suggested on another thread, I added something here.

]]>Initial stub to record some references. Wanted by type theoretic model category

]]>added some minimal properties

]]>gave *representation theory* a little Idea-section, then added some words on its incarnation as homotopy type theory in context/in the slice over $\mathbf{B}G$ and added the following *homotopy type representation theory – table*, which I am also including in other relevant entries:

homotopy type theory | representation theory |
---|---|

pointed connected context $\mathbf{B}G$ | ∞-group $G$ |

dependent type | ∞-action/∞-representation |

dependent sum along $\mathbf{B}G \to \ast$ | coinvariants/homotopy quotient |

context extension along $\mathbf{B}G \to \ast$ | trivial representation |

dependent product along $\mathbf{B}G \to \ast$ | homotopy invariants/∞-group cohomology |

dependent sum along $\mathbf{B}G \to \mathbf{B}H$ | induced representation |

context extension along $\mathbf{B}G \to \mathbf{B}H$ | |

dependent product along $\mathbf{B}G \to \mathbf{B}H$ | coinduced representation |

started some minimum

]]>To fulfil a link.

]]>I added a couple more references to Bayesian reasoning used in physics.

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]]>tried to polish algebraic definition of higher categories a little

]]>I got a 500 Internal Server Error trying to save the page duoidal category. I wanted to add some more details to the references as follows:

Marcelo Aguiar and Swapneel Mahajan,

*Monoidal Functors, Species and Hopf Algebras*, pdf. Here the notion is called a “2-monoidal category”.Richard Garner,

*Understanding the small object argument*, arXiv. Here the notion is called a “2-fold monoidal category”, although that term is also used for the case when the two units coincide.Michael Batanin and Martin Markl,

*Centers and homotopy centers in enriched monoidal categories.*Advances in Mathematics 230 , 4-6 (2012), 1811–1858. Here apparently the term “duoidal category” was introduced.Richard Garner, Ignacio López Franco,

*Commutativity*, arXiv. See also*Commutativity and tensor products of theories, monads, and operads*, talk at CT2013, slidesZoran Petrić and Todd Trimble 2014,

*Symmetric bimonoidal intermuting categories and $\omega \times \omega$ reduced bar constructions*, Applied Categorical Structures 22(3): 467-499, arXiv:0906.2954

On going back and canceling the edit, I got

```
XML Parsing Error: junk after document element
Location: https://ncatlab.org/nlab/cancel_edit/duoidal+category Line Number 4, Column 1:
<p><a href="https://ncatlab.org/nlab/show/HomePage">nLab home page</a></p>
^
```

and then again when trying to view the page to see if my edit took. But after a few seconds when I tried again I was able to view the page, and I see that my edit did not take.

]]>Split page from reflective factorization system, with some additional characterizations.

]]>I needed an entry to be able to point to which collects pointers to the various entries on “dualities” in string theory. So I created one: *duality in string theory*.

added to transferred model structure a simple remark in a subsection Enrichement on conditions that allow to transfer also an enriched model structure.

(The example I am thinking of is transferring the sSet-enriched model structure on cosimplicial rings to one on cosimplicial smooth algebras. But I won’t type that into the entry for the moment…)

]]>created algebraic model category

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]]>a bare minimum. One of these terms that people tend to use without bothering to recall its definition.

]]>**Edit to**: GUT by Urs Schreiber at 2018-04-01 01:21:13 UTC.

**Author comments**:

added pointer to textbook account

]]>Aleks Kissinger has contacted me about his aims to start a collection of nLab entries on quantum information from the point of view of the Bob Coecke school.

Being very much delighted about this offer, I created a template entry [[quantum information]] for his convenience.

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