Related papers: A Yoneda-Style Embedding for Virtual Equipments
In this article we develop formal category theory within augmented virtual double categories. Notably we formalise the classical notions of Kan extension, Yoneda embedding $\text y_A\colon A \to \hat A$, exact square, total category and…
Whereas formal category theory is classically considered within a $2$-category, in this paper a double-dimensional approach is taken. More precisely we develop such theory within the setting of augmented virtual double categories, a notion…
We prove an equivalence between cocomplete Yoneda structures and certain proarrow equipments on a 2-category $\mathcal K$. In order to do this, we recognize the presheaf construction of a cocomplete Yoneda structure as a relative, lax…
Notions and techniques of enriched category theory can be used to study topological structures, like metric spaces, topological spaces and approach spaces, in the context of topological theories. Recently in [D. Hofmann, Injective spaces…
In this article we are examining extensions and some basic diagrammatic properties of modules, in both cases from a new, "virtual" point of view. As natural background for investigating the kind of problems we are dealing with, the virtual…
It is well-known that the category of presheaf functors is complete and cocomplete, and that the Yoneda embedding into the presheaf category preserves products. However, the Yoneda embedding does not preserve coproducts. It is perhaps less…
In this article the notion of virtual double category (also known as fc-multicategory) is extended as follows. While cells in a virtual double category classically have a horizontal multi-source and single horizontal target, the notion of…
We introduce YOGA, a deep learning based yet lightweight object detection model that can operate on low-end edge devices while still achieving competitive accuracy. The YOGA architecture consists of a two-phase feature learning pipeline…
We propose a framework for producing interesting subcategories of the category ${}_A\mathsf{Mod}$ of left $A$-modules, where $A$ is an associative algebra over a field $k$. The construction is based on the composition, $Y$, of the Yoneda…
While virtual try-on for clothes and shoes with diffusion models has gained attraction, virtual try-on for ornaments, such as bracelets, rings, earrings, and necklaces, remains largely unexplored. Due to the intricate tiny patterns and…
We are studying properties of the name appointment in various categories of enriched graphs. The Yoneda lemma is generalized for continuous transforms between transports of enriched original graphs.
We provide various ways to characterise $\Sigma$-pure-injective objects in a compactly generated triangulated category. These characterisations mimic analogous well-known results from the model theory of modules. The proof involves two…
Recent advancements in image synthesis are fueled by the advent of large-scale diffusion models. Yet, integrating realistic object visualizations seamlessly into new or existing backgrounds without extensive training remains a challenge.…
We continue the study of enriched infinity categories, using a definition equivalent to that of Gepner and Haugseng. In our approach enriched infinity categories are associative monoids in an especially designed monoidal category of…
In this paper, we study the machine learning elements which we are interested in together as a machine learning system, consisting of a collection of machine learning elements and a collection of relations between the elements. The…
The proposed method extends upon the representational output of semantic instance segmentation by explicitly including both visible and occluded parts. A fully convolutional network is trained to produce consistent pixel-level embedding…
Just as the presheaf category is the free cocompletion of any small category, there is an analogous notion of free cocompletion for any small restriction category. In this paper, we extend the work on restriction presheaves to presheaves…
We propose a novel probabilistic model for visual question answering (Visual QA). The key idea is to infer two sets of embeddings: one for the image and the question jointly and the other for the answers. The learning objective is to learn…
We present Query2Prod2Vec, a model that grounds lexical representations for product search in product embeddings: in our model, meaning is a mapping between words and a latent space of products in a digital shop. We leverage shopping…
We show that the Yoneda embedding extends to an $(\infty,2)$-natural transformation. Furthermore, as such, it is uniquely determined by its value at the trivial $\infty$-category. We also study the naturality of the Yoneda lemma in its…