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Every book of mathematical logic should be a good reference where to find the notion of formula. Usually when one refers to formulas it means formulas of a first order language. A first order langua …

In every $n$-category (weak or strict) can be defined the concept of equivalence via a recursive definition: * an equivalence in a set ($0$-category) is just an identity; * for each $n \in \mathbb N$ …

I've read somewhere (probably in the nlab) that higher category theory has application in logic. By the way since now the only applications of higher category theory I've seen are in homotopy theory a …

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 …

The construction you describe seems more like the the category of reductions generated by the abstract rewrite system given by an algebraic theory. I suggest you take a look to section 8.2("Rewrite s …

Following the previous indication of Professor Brown I want to add another possible way to see natural transformation which is a generalization of the previous definition. Given categories $\mathc …

I doubt that someone could learn higher category theory (and more in general higher dimensional algebra) without first studying a little of category theory, mostly because the definition given in such …

The following question can be thought as a sequel of this one. Here I'm looking for a big list of example of weak algebraic structures: here weak means that the structure (i.e. operations) need not …

I've begun to interest in algebraic theories and their categorical models: in particular monads, generalized multicategories and operads, lawvere theories and their generalization. Is there any refere …

Every text book I've ever read about Category Theory gives the definition of natural transformation as a collection of morphisms which make the well known diagrams commute. There is another possible d …