5 papers
Tininess and right adjoints to exponentials
Enrique Ruiz Hernández, Pedro Solórzano
Objects whose exponential functor admits a right adjoint are known under different names. The fact that they exist, yet that the only set that satisfies this in…
A Categorical Generalization of Counterpoint
Octavio A. AgustÃn-Aquino, Juan Sebastián Arias, Enrique Ruiz Hernández
We extend Mazzola's counterpoint model using category theory, generalizing from the category to other topoi with suitable properties. This generalization suggests th…
Connectedness through decidable quotients
Enrique Ruiz Hernández, Pedro Solórzano
By looking at decidable quotients, a sufficient condition is provided to guarantee that (1) the full subcategory of decidable objects of a topos is an exponential ideal and that (2…
Naive homotopy theories in cartesian closed categories
Enrique Ruiz Hernández, Pedro Solórzano
An elementary notion of homotopy can be introduced between arrows in a cartesian closed category . The input is a finite-product-preserving endofunctor with a natural tra…
On logical parameterizations and functional representability in local set theories
Enrique Ruiz Hernández, Pedro Solórzano
There is a well-known inclusion of a topos in the linguistic topos of its internal language that proves both toposes to be equ…