Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Nunes, Fernando Lucatelli"'
Effective descent morphisms, originally defined in Grothendieck descent theory, form a class of special morphisms within a category. Essentially, an effective descent morphism enables bundles over its codomain to be fully described as bundles over it
Externí odkaz:
http://arxiv.org/abs/2410.22876
We study the categorical structure of the Grothendieck construction of an indexed category $\mathcal{L}:\mathcal{C}^{op}\to\mathbf{CAT}$ and characterise fibred limits, colimits, and monoidal structures. Next, we give sufficient conditions for the mo
Externí odkaz:
http://arxiv.org/abs/2405.07724
Publikováno v:
Theory Appl. Categ. 41(16):516-530, 2024
We investigate the properties of lax comma categories over a base category $X$, focusing on topologicity, extensivity, cartesian closedness, and descent. We establish that the forgetful functor from $\mathsf{Cat}//X$ to $\mathsf{Cat}$ is topological
Externí odkaz:
http://arxiv.org/abs/2405.03773
We consider the canonical pseudodistributive law between various free limit completion pseudomonads and the free coproduct completion pseudomonad. When the class of limits includes pullbacks, we show that this consideration leads to notions of extens
Externí odkaz:
http://arxiv.org/abs/2405.02185
We delve into the concept of categories with products that distribute over coproducts, which we call doubly-infinitary distributive categories. We show various instances of doubly-infinitary distributive categories aiming for a comparative analysis w
Externí odkaz:
http://arxiv.org/abs/2403.10447
Via the adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal V(1,-) \colon \mathsf{Span}(\mathcal V) \to \mathcal V \text{-} \mathsf{Mat} $ and a cartesian monad $ T $ on an extensive category $ \mathcal V $ with finite limits, we construct an adjunct
Externí odkaz:
http://arxiv.org/abs/2309.08084
Publikováno v:
Quaestiones Mathematicae, 46:sup1, 145-159 (2023)
Let $\mathsf{Ord} $ be the category of (pre)ordered sets. Unlike $\mathsf{Ord}/X$, whose behaviour is well-known, not much can be found in the literature about the lax comma 2-category $\mathsf{Ord} //X$. In this paper we show that the forgetful func
Externí odkaz:
http://arxiv.org/abs/2212.13541
Publikováno v:
Bull. Belg. Math. Soc. Simon Stevin 30(1): 130-139 (july 2023)
For any suitable base category $\mathcal{V} $, we find that $\mathcal{V} $-fully faithful lax epimorphisms in $\mathcal{V} $-$\mathsf{Cat} $ are precisely those $\mathcal{V}$-functors $F \colon \mathcal{A} \to \mathcal{B}$ whose induced $\mathcal{V}
Externí odkaz:
http://arxiv.org/abs/2210.12021
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 categorical semantics. We demonstrate how it can be used to give a very stra
Externí odkaz:
http://arxiv.org/abs/2210.08530
We give a simple, direct and reusable logical relations technique for languages with term and type recursion and partially defined differentiable functions. We demonstrate it by working out the case of Automatic Differentiation (AD) correctness: name
Externí odkaz:
http://arxiv.org/abs/2210.07724