Related papers: Coequalisers under the Lens
We show that the category of simplicial sets is a co-reflective subcategory of the category of cubical sets with connections, with the inclusion given by a version of the straightening functor. We show that using the co-reflector, one can…
A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. In \cite{DR2} we gave characterizations of monomorphisms (resp. epimorphisms) in arbitrary pro-categories, pro-(C), where (C) has…
Experience shows that the poset of levels (or dimensions) of the topos of presheaves on some elegant Reedy categories may be equipped with a monotone increasing `successor' function which, as the case of simplicial sets shows, is different…
Conventional object detectors rely on cross-entropy classification, which can be vulnerable to class imbalance and label noise. We propose CLIP-Joint-Detect, a simple and detector-agnostic framework that integrates CLIP-style contrastive…
Continual learning allows a model to learn multiple tasks sequentially while retaining the old knowledge without the training data of the preceding tasks. This paper extends the scope of continual learning research to class-incremental…
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…
All-optical information communication, processing and computation have received substantial interest of both fundamental and applied research due to its unrivaled speed and broad bandwidth. Compared to its electronic counterpart, photons…
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, i.e. monads and comonads in a monoidal category such that the endofunctor of the monad or comonad is a monoidal functor…
Many contrastive and meta-learning approaches learn representations by identifying common features in multiple views. However, the formalism for these approaches generally assumes features to be shared across views to be captured…
We present a way of constructing a Quillen model structure on a full subcategory of an elementary topos, starting with an interval object with connections and a certain dominance. The advantage of this method is that it does not require the…
We prove that for a large class of well-behaved cocomplete categories $\mathcal C$ the weak and strong Drinfeld centers of the monoidal category $\mathcal{E}$ of cocontinuous endofunctors of $\mathcal{C}$ coincide. This generalizes similar…
We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…
We apply a categorical lens to the study of betweenness relations by capturing them within a topological category, fibred in lattices, and study several subcategories of it. In particular, we show that its full subcategory of finite objects…
Let $\Lambda$ be the category of based finite sets $\mathbf{n}$ and based injections. We study properties of monoids and modules in $\Lambda$-sequences under the Kelly monoidal structure. In particular, we show that the forgetful functor…
We give a characterisation of functors whose induced functor on the level of localisations is an equivalence and where the isomorphism inverse is induced by some kind of replacements such as projective resolutions or cofibrant replacements.
Overlapping sound events are ubiquitous in real-world environments, but existing end-to-end sound event detection (SED) methods still struggle to detect them effectively. A critical reason is that these methods represent overlapping events…
We distinguish between faint, weak, strong and strict localizations of categories at morphism families and show that this framework captures the different types of derived functors that are considered in the literature. More precisely, we…
A distinction is often drawn between a model's ability to predict a label for an evaluation sample that is directly memorised from highly similar training samples versus an ability to predict the label via some method of generalisation. In…
We show that the left regular representation \pi_l of a discrete quantum group (A,\Delta) has the absorbing property and forms a monoid (\pi_l,\tilde{m},\tilde{\eta}) in the representation category Rep(A,\Delta). Next we show that an…
Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…