17 citations · 54 across the 12 of their papers we have counts for
15 papers
Absolute descent and the Bénabou--Roubaud theorem
Fernando Lucatelli Nunes
We continue the programme developed in Pseudo-Kan extensions and descent theory by studying descent for augmented pseudocosimplicial objects. Let be a -category, an…
Cartesian closedness of lax comma categories
Maria Manuel Clementino, Fernando Lucatelli Nunes
For a finitely complete category X, we prove that the lax comma category Cat//X is cartesian closed if and only if its free coproduct completion Fam(X) is cartesian closed. The pro…
From Grothendieck cofibrations to factorization systems: a formal 2-monadic account
Fernando Lucatelli Nunes, Walter Tholen
Grothendieck cofibrations describe transport in a category varying over a base, while factorization systems organize the arrows of a category into two complementary classes. We giv…
Lax comma categories of ordered sets
Maria Manuel Clementino, Fernando Lucatelli Nunes
Let be the category of (pre)ordered sets. Unlike , whose behaviour is well-known, not much can be found in the literature about the lax comma 2-cate…
Logical Relations for Partial Features and Automatic Differentiation Correctness
Fernando Lucatelli Nunes, Matthijs Vákár
We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in catego…
Cauchy Completeness, Lax Epimorphisms and Effective Descent for Split Fibrations
Fernando Lucatelli Nunes, Rui Prezado, Lurdes Sousa
For any suitable base category , we find that -fully faithful lax epimorphisms in - are precisely those -funct…
Descent for internal multicategory functors
Rui Prezado, Fernando Lucatelli Nunes
We give sufficient conditions for effective descent in categories of (generalized) internal multicategories. Two approaches to study effective descent morphisms are pursued. The fi…
CHAD for Expressive Total Languages
Fernando Lucatelli Nunes, Matthijs Vákár
We show how to apply forward and reverse mode Combinatory Homomorphic Automatic Differentiation (CHAD) to total functional programming languages with expressive type systems featur…
Lax comma -categories and admissible -functors
Maria Manuel Clementino, Fernando Lucatelli Nunes
This paper is a contribution towards a two dimensional extension of the basic ideas and results of Janelidze-Galois theory. In the present paper, we give a suitable counterpart not…
Descent Data and Absolute Kan Extensions
Fernando Lucatelli Nunes
The fundamental construction underlying descent theory, the lax descent category, comes with a functor that forgets the descent data. We prove that, in any -category $\mathfrak{…
Pseudomonads and Descent, PhD Thesis (Chapter 1)
Fernando Lucatelli Nunes
This is the introductory chapter of my PhD Thesis. This thesis consists of one introductory chapter and four single-authored papers written during my PhD studies at the University…
Freely generated -categories, coinserters and presentations of low dimensional categories
Fernando Lucatelli Nunes
A presentation records not only a categorical structure but also how it is assembled. This matters for rewriting, coherence, and minimality: freely adjoining a cell with prescribed…
On lifting of biadjoints and lax algebras
Fernando Lucatelli Nunes
By the biadjoint triangle theorem, given a pseudomonad on a -category , if a right biadjoint has a lifting to the ps…
On biadjoint triangles
Fernando Lucatelli Nunes
We prove a biadjoint triangle theorem and its strict version, which are -dimensional analogues of the adjoint triangle theorem of Dubuc. Similarly to the -dimensional case, w…
Pseudo-Kan Extensions and Descent Theory
Fernando Lucatelli Nunes
There are two main constructions in classical descent theory: the category of algebras and the descent category, which are known to be examples of weighted bilimits. We give a form…