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    • Page created. Feel free to add to or reorganize the content!

      v1, current

    • New page in order to drop some references.

      v1, current

    • Created categorical model of dependent types, describing the various different ways to strictify category theory to match type theory and their interrelatedness. I wasn’t sure what to name this page — or even whether it should be part of some other page — but I like having all these closely related structures described in the same place.

    • added to Grothendieck construction a section Adjoints to the Grothendieck construction

      There I talk about the left adjoint to the Grothendieck construction the way it is traditionally written in the literature, and then make a remark on how one can look at this from a slightly different perspective, which then is the perspective that seamlessly leads over to Lurie's realization of the (oo,1)-Grothendieck construction.

      There is a CLAIM there which is maybe not entirely obvious, but straightforward to check. I'll provide the proof later.

    • Page created for now. More content to be added soon.

      v1, current

    • the standard bar complex of a bimodule in homological algebra is a special case of the bar construction of an algebra over a monad. I have added that as an example to bar construction.

      I also added the crucial remark (taken from Ginzburg’s lecture notes) that this is where the term “bar” originates from in the first place: the original authors used to write the elements in the bar complex using a notaiton with lots of vertical bars (!).

      (That’s a bad undescriptive choice of terminoiogy. But still not as bad as calling something a “triple”. So we have no reason to complain. ;-)

    • added pointer to today’s

      • Krzysztof Andrzejewski, Cezary Gonera, Joanna Goner, Piotr Kosinski, Pawel Maslanka, Spinning particles, coadjoint orbits and Hamiltonian formalism (arXiv:2008.09478)

      diff, v16, current

    • I have expanded various sections at disjoint coproduct. In particular towards the end is now a mentioning of the fact that in a positive category morphisms into a disjoint coproduct are given by factoring disjoint summands of the domain through the canonical inclusions.

      Also,I made positive category and variants redirect to extensive category.

    • Added a reference to

      • Christian Maurer, Universes in Topoi , pp.285-296 in Lawvere, Maurer, Wraith (eds.), Model Theory and Topoi , LNM 445 Springer Heidelberg 1975.

      diff, v19, current

    • stub for Chern character

      just the blind definition so far, to be expanded later

    • added to equivariant K-theory comments on the relation to the operator K-theory of crossed product algebras and to the ordinary K-theory of homotopy quotient spaces (Borel constructions). Also added a bunch of references.

      (Also finally added references to Green and Julg at Green-Julg theorem).

      This all deserves to be prettified further, but I have to quit now.

    • Added a reference to

      • John W. Gray, Coherence for the Tensor Product of 2-Categories, and Braid Groups , pp.62-76 in Heller, Tierney (eds.), Algebra, Topology, and Category Theory , Academic Press New York 1976.

      diff, v19, current

    • some minimum, just for completeness

      v1, current

    • edited classifying topos and added three bits to it. They are each marked with a comment "check the following".

      This is in reaction to a discussion Mike and I are having with Richard Williamson by email.

    • Created a page for the homonymous cartesian theory.

      v1, current