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There is a notion of 'oidification' in category theory which characterises many object versions of mathematical objects. For example: magmas $\rightarrow$ magmoids loops $\rightarrow$ loopoids grou …

I answered this question on "is there a longest geodesic" by a kind of a joke, which I couldn't resist: the long line! Simply going by the name it had to be the 'longest geodesic'! I didn't bother exp …

Most of the references I've seen deal with Riemannian geometry, rather than semi-Riemannian geometry. Chens monograph, Pseudo-Riemannian Geometry, $\Delta$-Invariants and Applications is one of the fe …

In Veltman's Diagrammatica, the full Lagrangian of the standard model is spelt out. This has around a hundred terms. This is way too many for even the most dedicated physicist (or physically inclined …

I'm currently reading Michor, Manifold of Mappings for Continuum Mechanics. In this paper he makes use of 'Whitney Jets' but takes it to be an already understood concept. I'm familiar with jets but ha …

In Borceaux and Janelidze's Galois Theories, a construction of the Pierce spectrum is given. It is the poset of ideals in a Boolean ring. It's construction is reminiscent of the Zariski spectrum in co …

There is such a thing as Algebraic Set Theory where: models of set theory are simply algebras for a suitably presented algebraic theory and then many familiar set theoretic conditions (such as well-f …

An essay of mine which won a special creative writing prize at FXQi was published by Springer in their Frontiers collection, What is Fundamental? I extended my essay for the volume and it included a m …

Gyrogroups were discovered by Ungar in modelling the Einstein velocity addition rule in relativity. Have they been shown to be useful elsewhere in mathematics (or mathematical physics)?

I recently got interested in the same question. You've probably come across Picado & Pultr's Frames & Locales where they describe these technicalities but not in the context of putting them together t …

There are three that I can think: Brian Hall, Quantum Theory for Mathematicians. and Sachs & Wu, General Relativity for Mathematicians Also Saunders Mac Lane, Categories for the Working Mathematician …

Try the book by Michor, Kolar & Slovak titled Natural Operations in Differential Geometry, it's rather dense so if you're uncomfortable with Kobayashi & Nomizu you might find it doesn't work for you. …

This is just a reference request. I thought I'd come across a paper demonstrating that there is a translation invariant measure on an infinite-dimensional space without 'points' whilst browsing the ne …

Alice Rogers Supermanifolds is a rigorous introduction to supermanifolds in the geometric and algebraic approaches with the emphasis on the geometric. She also discusses applications to physics such a …

This is just a reference request. I came across an NLab page on particle species described as certain vector bundles. But I can't seem to find it again when I searched recently. If someone can point o …