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Is there a way to recapture the additional understanding imparted by multicategories using higher categories? Well I would say so. Multicategories are basically categories whose morphisms have multi …

I am not aware of Kock's works. Nevertheless Kelly provides the definition of its tensor product in the next page: it defines its tensor product $\mathcal A \otimes_{\mathcal F} \mathcal B$ as the $\ …

I am not an expert on the subject but looking at the definition I would dare to say that these are basically the axioms that characterize an homology theory, if it weren't for the fact the $\delta$ ma …

I suppose that there are possibly many different answer to this question. Here is the one I got. Being a reflector is equivalent to being an inclusion that has a left adjoint. In general being a co …

I cannot say what exactly Voevodsky meant but here is a wild guess. Disclaimer in what follows I use heavily type theoretic notation, so you have trouble understanding feel free to ask in the comment …

I have posted this question here on M.SE but since it received little attention and since it seems difficult to find helpfule references I reposting it here. In Jacob's Categorical logic and Type The …

I see that this question has an already accepted answer but I think that may be of interest. There is a notion of category with internal hom with no reference to a monoidal structure, that is the not …

I think there can be no easy answer to your question or to be exact I'm afraid that there are many different reasons for using universes instead of sticking with just one foundational set theory. I w …

I think the idea should pretty much like this: once you drop the requirement for the deductive system to be freely generated from the axioms by the inference rules (i.e. you accept the existence of no …

Could anyone explain what higher dimensional algebra is? I tried to look on the web but I couldn't find a satisfactory definition, the ones that I found are too vague. What I'm looking for is a good …

If I understand correctly your question you are looking for some definition of limit-sketches such that if two sketches $\mathcal T$ and $\mathcal T'$ are Morita-equivalent (that is the categories of …

Maybe this doesn't address completly to the question, but I think it's a start. Functor categories and higher categories are quite different objects, the only relation that I can think of is that usu …

By Yoneda for every natural transformation $\tau \colon \mathbf C(c,-) \to F$, where $F \colon \mathbf C \to \mathbf{Set}$ and $\mathbf C(c,-)$ is the covariant $\hom$-functor, is a family of function …

This question want to be a follow up of the following question. In that thread I was interested in understanding relation between various presentation of algebraic theories. In particular in Eduardo P …

Well the two monads are quite different: in May definition you deal with an actual monad in $\mathbf {Cat}$ (i.e. a strict-$2$-category) while in the second case you work with monads in the bicategory …