Before changing the PROP entry to add this variant, i would like to have a nice reference on this. ]]>

a bare list of references, to be `!include`

-ed into the References-section of relevant entries (such as at *braid group representation* and at *semi-metal*).

Had originally compiled this list already last April (for this MO reply) but back then the nLab couldnt be edited

]]>Described the free suplattice on a poset.

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brief `category:people`

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I have added to *monoidal model category* statement and proof (here) of the basic statement:

Let $(\mathcal{C}, \otimes)$ be a monoidal model category. Then 1) the left derived functor of the tensor product exsists and makes the homotopy category into a monoidal category $(Ho(\mathcal{C}), \otimes^L, \gamma(I))$. If in in addition $(\mathcal{C}, \otimes)$ satisfies the monoid axiom, then 2) the localization functor $\gamma\colon \mathcal{C}\to Ho(\mathcal{C})$ carries the structure of a lax monoidal functor

$\gamma \;\colon\; (\mathcal{C}, \otimes, I) \longrightarrow (Ho(\mathcal{C}), \otimes^L , \gamma(I)) \,.$The first part is immediate and is what all authors mention. But this is useful in practice typically only with the second part.

]]>am finally giving this its own entry, to be split off (not done yet) from *D-brane charge* and to be in parallel with *K-theory classification of topological phases of matter*

brief `category:people`

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brief `category:people`

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a stub entry, for the moment just in order to satisfy links

]]>stub for *quantum computation*

starting a `category:reference`

-page in which to eventually collect pointers to the contributions to this upcoming book collection

this page needs attention. For the moment I have at least added these original articles:

Michael Atiyah, Isadore Singer,

*Index theory for skew-adjoint Fredholm operators*, Publications Mathématiques de l’IHÉS, Tome**37**(1969) 5-26 $[$numdam:PMIHES_1969__37__5_0$]$Max Karoubi,

*Espaces Classifiants en K-Théorie*, Transactions of the American Mathematical Society**147**1 (Jan., 1970) 75-115 $[$doi:10.2307/1995218$]$

Added a new Properties section to connected object. Including a theorem which is a bit of a hack (where I leave it to others to decide if ’hack’ should be interpreted positively or negatively!).

]]>brief `category:people`

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a stub

]]>splitting this off from *su(2)-anyons*: Copied much of the material over, but also added a few more sentences.

For the moment this entry is a cautionary tale about confirmation bias more than an entry about physics.

]]>brief `category:people`

-entry for hyperlinking references at *tensor hierarchy* and at *Borcherds algebra*

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 |

added pointer to:

- Peter Draxl,
*Skew fields*, London Math. Soc. Lecture notes**81**, Cambridge University Press 1983 (doi:10.1017/CBO9780511661907, ISBN:9780511661907)

The shriek/star notation for existential and universal quantification was backwards from the usual conventions (which are: lower shriek for left adjoint to base change, lower star for right adjoint to base change).

]]>brief `category:people`

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brief `category:people`

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starting a `category:reference`

-entry.

Just a single item so far, but this entry should incrementally grow as more preprints appear (similar to what we have been doing at *Handbook of Quantum Gravity* and similar entries).

I know that a soft deadline for submissions of at least one of the sections is this December, so I am guessing this is planned to appear in 2024.

]]>brief `category:people`

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