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I'm familiar with the tensor product of modules, but I've also come across functor tensor product (in emily riehls paper on homotopy limits), what are they, and how are they (if they are) related to t …

I'm having trouble understanding what classifying spaces are in general. It seems to me, that they are terminal in a category of bundles whose morphisms are pullback squares, is this correct?

Let A & B be two categories, the join A*B is created by stipulating its class of object is the disjoint union of the objects of A & B, the morphisms remain the 'same', but we throw in an extra morphi …

I'm having trouble understanding the definition of Verma Module in wikipedia. It later goes to show that it satisfies what appears to be a universal property (which I'm also having trouble understandi …

Complement Toposes are dual in a sense to (elementary) Toposes and are expected to have typed higher paraconsistent logic as its internal language (as dual intuitionistic logic is paraconsistent). No …

Is the gluing of bundles from not-necessarily trivial bundles just some kind of 2-colimit?

not my answer, but David Carchedi's answer in a comment: 'What you might be thinking is, the category of principal bundles over a fixed base is a 2-colimit over all covers of the base (or some cofina …

The category of convergence spaces generalise topological spaces and form a quasi-topos, as topoi are allegedly nicer is there a nicer kind of topological-like space, the category of which forms a top …

I've just beginning to learn logic and proof theory - and the following rather vague and perhaps ill-formed question occurred to me. Given an alphabet it's straightforward to construct the Language, …

Grothendieck universes are equivalent to ZFC+a strongly inaccessible cardinal. This is low on the large cardinal axiom list. Is it enough to place category theory on a firm foundational basis, and how …

Lurie's book, higher topos theory describes a new notion of a triangulated category, which is apparently much more natural than the usual definition. Obviously by now a great deal of work has been don …

Immersions & sumersions are important in differential manifolds. They rely on their definition of the construction of the tangent bundle. I realise that generalised smooth spaces do not have a canoni …

the unadorned typed lambda calculus correspond to the closed cartesian categories, but if we add in dependent or parametric types how are they then characterised?

First-order order classical logic with standard semantics has a proof theory: it is complete, sound and effective. In higher order logic with standard semantics one cannot obtain a proof theory - i …

I found the Catsters on YouTube divinely useful. John Baez, in his not so weekly blog, inspiring. The n-category cafe, to keep you going. Eugenia Cheng's notes on category theory was tremendously u …