switching to latex notation for sections and subsections

Anonymous

]]>Tried to bring the list of references under “Textbooks – Basic category theory” (here) into chronological order and added a bunch of missing links. (room left to polish this up further…)

]]>added pointer to

- Colin McLarty,
*Elementary Categories, Elementary Toposes*, Oxford University Press 1992 (ISBN:9780198514732)

and re-arranged the other items around it into chronological order (here)

]]>added pointer to:

- Chris Heunen, Jamie Vicary,
*Categories for Quantum Theory*, Oxford University Press 2019 (ISBN:9780198739616)

added pointer to:

- Martin Brandenburg,
*Einführung in die Kategorientheorie*, Springer 2017 (doi:10.1007/978-3-662-53521-9)

added ISBN to

- Robert Geroch,
*Mathematical Physics*, Chicago 1985 (ISBN:9780226223063)

and DOI to

- Marco Grandis,
*Category Theory and Applications: A Textbook for Beginners*, World Scientific 2021 (doi:10.1142/12253)

Added a reference to Joyal’s CatLab.

]]>added publication data for

- Birgit Richter,
*From categories to homotopy theory*, Cambridge Studies in Advanced Mathematics 188, Cambridge University Press 2020 (doi:10.1017/9781108855891, book webpage, pdf)

As suggested on another thread, I have added in a reference to the list of networks of category theorists. It could be useful.

]]>Added a reference to lectures on category theory by Peter Johnstone.

]]>Raymond, if you have javascript disabled and are not using a browser such as Firefox which can render MathML, you may encounter this. To render mathematics one needs one of the two.

]]>I have removed the “other texts”-label.

]]>replaced the dead link to Barr-Wells TTT with a link to the TAC reprint. Also I wonder why it is listed under “other texts”.

]]>Do you mean a specific entry, or is it the $n$Lab in general that does not display properly on your system?

I just checked the entry *category theory*, and – except for some bad whitespaces, which I have fixed now – it renders properly on my system.

Can this be corrected?

Regards,

Raymond Boute ]]>

Mention additional non-mathematical applications of CT; reference ’applied category theory’ page.

]]>Add link to Grandis’s textbook

]]>I still want to know in the progression of the modalities why jets rather than germs?. Should minimality tell us which?

]]>Well, density is something that can be expressed internally.

]]>Ignoring the Hegelese, is this not a mathematical use of minimality at Aufhebung?

]]>…the Aufhebung of $\emptyset\dashv \ast$ is necessarily given by a

densesubtopos $\mathcal{E}_j$. Since the double negation topology $\neg\neg$ is the unique largest dense topology it follows in general that $\mathcal{E}_{\neg\neg}\subseteq\mathcal{E}_j$ , in particular in the case that $\mathcal{E}_{\neg\neg}$ happens to be essential and hence happens to be a level, the minimality condition on the Aufhebung of the initial opposition means that $\mathcal{E}_j = \mathcal{E}_{\neg\neg}$ is, in particular, a Boolean topos.

I’m glad Dan’s talk was helpful, Urs!

]]>the minimality aspect of the progression couldn’t be represented in 2-DTT.

Is there any *mathematical* use for that minimality?

Type theory seems to have that effect.

By the way, where you hope in #29

Maybe there could be a type theory which is adjoint-to-the-roots that would be able to more seamlessly admit implementation of progressions of adjoint modalities as needed for super-differential cohesion.

I asked something to that effect on the blog, and Mike pointed out that the minimality aspect of the progression couldn’t be represented in 2-DTT.

]]>Okay, this morning I heard Dan Licata’s very nice talk (here) on LSR and followup developments. Towards the end it had something about the “Modal theory of Dependent type theory”, which seems to be exactly the kind of thing I was expressing hope, above, should exist, and should help with defining adjoint modalities in DTT.

I don’t quite understand now the way the discussion worked out here (apparently various misunderstandings) but I am very happy to see this take shape!

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