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So, here are some definitions about Natural Numbers Object (nno), that is a key concept in category theory related to Computer Science. They are given in Lambek and Scott (LS) in the following form: …

An equalizer in a category $\mathcal{C}$ is a couple $(E,eq)$ consisting in an object $E$ and a morphism $eq:E\longrightarrow X$ so that $f\circ eq=g\circ eq$ for every pair of parallel morphisms $f,g …

Lambek and Scott demonstrate in Introduction to higher order categorical logic the existence of a parametrized nno when we are in a cartesian closed category (CCC) with a "simple nno" and suggest the …

Hello, I'm writting something about Malcev categories and monadicity. The fact is that I need to know if Graph is or not complete (have all finite limits). It seems easy but I would like a real answer …

Under which conditions can we say that the cotensor objects in a (closed) V-category are the exponential objects? It is just when V=Set?

Since a pullback of two functions f and g with common codomain into Set category is just a subset of cartesian product like this: {(x,y)/f(x)=g(y)} (with two more functions not important here) could t …

As far as I now (correct me if I'm wrong, please): 1 The recursive topos was introduced in "The topos of recursive sets", Thesis, Buffalo, 1980. It is $Rec=Sh_{J}(Set^{M^{op}})$ where: -M is the mo …

I’ve couldn’t find any information about the free category built up from that Freyd cover. Where can I find more about the Freyd cover of a category (not a topos!)? Edit: The definition has been giv …

Can anybody give a definition of the equalizer completion of a cartesian category? Is the method to get more or less as the regular and exact completions in the way that are given in: http://ncatlab …

It is known that the codomain fibration is given by a functor in the form $\mathcal{C}^{\rightarrow}\longrightarrow\mathcal{C}$ where $\mathcal{C}$ is a category having pullbacks and $\mathcal{C}^{\r …

I would like to know which is the real difference between the Recursive topos (in the sense of Mulry) and the Effective topos (in the sense of Hyland). Especially what is related to recursive function …

What does a coequalizer in the category of primitive recursive functions look like? I know that in Set, a coequalizer is a minimum congruence but...what is it in particular in the category of primitiv …