Related papers: Injective and Projective Model Structures on Enric…
We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability. The main result, which was known for…
Recursive graph queries are increasingly popular for extracting information from interconnected data found in various domains such as social networks, life sciences, and business analytics. Graph data often come with schema information that…
It is well-known that combinatorial circuits are modeled mathematically by string diagrams in a monoidal category. Given a gate set $\Sigma$, the circuits over $\Sigma$ can be thought of as string diagrams in the free monoidal category…
This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…
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…
We prove an adjoint functor theorem in the setting of categories enriched in a monoidal model category $\mathcal V$ admitting certain limits. When $\mathcal V$ is equipped with the trivial model structure this recaptures the enriched…
We prove that, under certain conditions, the model structure on a monoidal model category $\mathcal{V}$ can be transferred to a model structure on the category of $\mathcal{V}$-enriched coloured (symmetric) operads. As a particular case we…
This paper develops a theory of colimit sketches "with constructions" in higher category theory, formalising the input to the ubiquitous procedure of adjoining specified "constructible" colimits to a category such that specified "relation"…
Enriched categories are categories whose sets of morphisms are enriched with extra structure. Such categories play a prominent role in the study of higher categories, homotopy theory, and the semantics of programming languages. In this…
In this paper we present background results in enriched category theory and enriched model category theory necessary for developing model categories of enriched functors suitable for doing functor calculus.
We observe that the Reedy model structure on a diagram category can be constructed by iterating an operation of "bigluing" model structures along a pair of functors and a natural transformation. This yields a new explanation of the…
Building on our previous work on enriched regular logic, we introduce an enriched version of positive logic and relate it to enriched cone-injectivity classes and enriched accessible categories. To do this, we need a factorization system on…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
We prove that the projective model structure on the category of unbounded cochain complexes extends naturally to the category of contractions. The proof is completely elementary and we do not assume familiarity with model categories.
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…
In this work, we explore a double categorical framework for categories of enriched graphs, categories and the newly introduced notion of cocategories. A fundamental goal is to establish an enrichment of V-categories in V-cocategories, which…
We show that for various natural classes of groups and appropriately defined K- and L-theoretic functors, injectivity or bijectivity of the assembly map follows from the Isomorphism Conjecture being true for acyclic groups lying within that…
In this short note we show that E-infinity quasi-categories can be replaced by strictly commutative objects in the larger category of diagrams of simplicial sets indexed by finite sets and injections. This complements earlier work on…
We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of…
The theory of presentations of enriched monads was developed by Kelly, Power, and Lack, following classic work of Lawvere, and has been generalized to apply to subcategories of arities in recent work of Bourke-Garner and the authors. We…