Zobrazeno 1 - 10
of 142
pro vyhledávání: '"Rosicky, Jiri"'
Autor:
Kamsma, Mark, Rosický, Jiří
Given a functor $F: \mathcal{C} \to \mathcal{D}$ and a model-theoretic independence relation on $\mathcal{D}$, we can lift that independence relation along $F$ to $\mathcal{C}$ by declaring a commuting square in $\mathcal{C}$ to be independent if its
Externí odkaz:
http://arxiv.org/abs/2411.14813
Autor:
Rosický, Jiří
We show that, under certain assumptions, strongly finitary enriched monads are given by discrete enriched Lawvere theories. On the other hand, monads given by discrete enriched Lawvere theories preserve surjections.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2411.02841
Autor:
Rosický, Jiří, Tendas, Giacomo
Building on our previous work on enriched universal algebra, we define a notion of enriched language consisting of function and relation symbols whose arities are objects of the base of enrichment. In this context, we construct atomic formulas and de
Externí odkaz:
http://arxiv.org/abs/2406.12617
Autor:
Kamsma, Mark, Rosický, Jiri
We give a category-theoretic construction of simple and NSOP$_1$-like independence relations in locally finitely presentable categories, and in the more general locally finitely multipresentable categories. We do so by identifying properties of a cla
Externí odkaz:
http://arxiv.org/abs/2310.15804
Autor:
Rosický, Jiří, Tendas, Giacomo
Following the classical approach of Birkhoff, we suggest an enriched version of enriched universal algebra. Given a suitable base of enrichment $\mathcal V$, we define a language $\mathbb L$ to be a collection of $(X,Y)$-ary function symbols whose ar
Externí odkaz:
http://arxiv.org/abs/2310.11972
Autor:
Mazari-Armida, Marcos, Rosicky, Jiri
We study classes of modules closed under direct sums, $\mathcal{M}$-submodules and $\mathcal{M}$-epimorphic images where $\mathcal{M}$ is either the class of embeddings, $RD$-embeddings or pure embeddings. We show that the $\mathcal{M}$-injective mod
Externí odkaz:
http://arxiv.org/abs/2308.02456
Autor:
Rosický, Jiří, Tendas, Giacomo
We introduce the enriched notions of purity depending on the left class $\mathcal E$ of a factorization system on the base $\mathcal V$ of enrichment. The ordinary purity is given by the class of surjective mappings in the category of sets. Under spe
Externí odkaz:
http://arxiv.org/abs/2303.11957
Quillen's notion of small object and the Gabriel-Ulmer notion of finitely presentable or generated object are fundamental in homotopy theory and categorical algebra. Do these notions always lead to rather uninteresting classes of objects in categorie
Externí odkaz:
http://arxiv.org/abs/2302.00050
Autor:
Rosický, Jiří
The category $Ban$ of Banach spaces and linear maps of norm $\leq 1$ is locally $\aleph_1$-presentable but not locally finitely presentable. We prove, however, that $Ban$ is locally finitely presentable in the enriched sense over complete metric spac
Externí odkaz:
http://arxiv.org/abs/2206.08546
Autor:
Rosický, Jiří
We introduce discrete equational theories where operations are induced by those having discrete arities. We characterize the corresponding monads as monads preserving surjections. Using it, we prove Birkhoff type theorems for categories of algebras o
Externí odkaz:
http://arxiv.org/abs/2204.02590