Related papers: Lax Functors, Cospans, and the Center Construction
For any algebra morphism in a monoidal category, we provide sufficient conditions (which are also necessary if the unit is a left tensor generator) for the attached induction functor being semiseparable. Under mild assumptions, we prove…
Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible.
We construct the reflection functors for quiver Hecke algebras of an arbitrary symmetrizable Kac-Moody type. These reflection functors categorify Lusztig's braid symmetries.
In this paper we prove a few propositions concerning factorizations of morphisms in pro categories, the most important of which solves an open problem of Isaksen concerning the existence of certain types of functorial factorizations. On our…
We show how the tangent functor extends from ordinary smooth maps to "microformal morphisms" (also called "thick morphisms") of supermanifolds. Microformal morphisms generalize ordinary maps and correspond to formal canonical relations…
Relative theories(=closed subfunctors) are considered in exact, triangulated and extriangulated categories by Dr\"{a}xler-Reiten-Smal{\o}-Solberg-Keller, Beligiannis and Herschend-Liu-Nakaoka, respectively. We give a construction method of…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
In this work we discuss a new type of factorisation systems for \textbf{Ord}-enriched categories. We start by defining the new notion of lax weak orthogonality, which involves the existence of lax diagonal morphisms for lax squares. Using…
It is shown that every concretizable category can be fully embedded into the category of accessible set functors and natural transformations.
Generic notions of bisimulation for various types of systems (nondeterministic, probabilistic, weighted etc.) rely on identity-preserving (normal) lax extensions of the functor encapsulating the system type, in the paradigm of universal…
We generalize and greatly simplify the approach of Lydakis and Dundas-R\"ondigs-{\O}stv{\ae}r to construct an L-stable model structure for small functors from a closed symmetric monoidal model category V to a V-model category M, where L is…
We give a general construction of realization functors for $t$-structures on the base of a strong stable derivator. In particular, given such a derivator $\mathbb D$, a $t$-structure $\mathbf t=(\mathcal D^{\leq0},\mathcal D^{\geq0})$ on…
We define two functors from Elias and Khovanov's diagrammatic Soergel category, one targeting Clark-Morrison-Walker's category of disoriented sl(2) cobordisms and the other the category of (universal) sl(3) foams.
We study hearts of cotorsion pairs in triangulated and exact categories.We give a sufficient and necessary condition when the hearts have enough projectives. We also show in such condition they are equivalent to functor categories over…
A TQFT is a functor from a cobordism category to the category of vector spaces, satisfying certain properties. An important property is that the vector spaces should be finite dimensional. For the WRT TQFT, the relevant 2+1-cobordism…
It is known that the Grothendieck group of the category of Schur functors is the ring of symmetric functions. This ring has a rich structure, much of which is encapsulated in the fact that it is a "plethory": a monoid in the category of…
The construction of the universal ring of Witt vectors is related to Lazard's factorizations of free monoids by means of a noncommutative analogue. This is done by associating to a code a specialization of noncommutative symmetric…
Given a cohomological functor from a triangulated category to an abelian category, we construct under appropriate assumptions for any localization functor of the abelian category a lift to a localization functor of the triangulated…
Given 2-categories $\mathcal{C}$ and $\mathcal{D}$, let $\textrm{Lax}(\mathcal{C},\mathcal{D})$ denote the 2-category of lax functors, lax natural transformations and modifications, and $[\mathcal{C},\mathcal{D}]_\mathrm{lnt}$ its full…
We construct an $(\infty,2)$-version of the (lax) Gray tensor product. On the 1-categorical level, this is a binary (or more generally an $n$-ary) functor on the category of $\Theta_2$-sets, and it is shown to be left Quillen with respect…