Related papers: Locally Cartesian Closed Categories
Categorical enumerative invariants of a Calabi-Yau category, encoded as the partition function of the associated closed string field theory (SFT), conjecturally equal Gromov-Witten invariants when applied to Fukaya categories. Part of this…
There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms…
Cartesian differential categories are categories equipped with a differential combinator which axiomatizes the directional derivative. Important models of Cartesian differential categories include classical differential calculus of smooth…
We introduce a new categorical framework for studying derived functors, and in particular for comparing composites of left and right derived functors. Our central observation is that model categories are the objects of a double category…
This work mainly concerns the -- here introduced -- category of $\mathscr Q$-sets and functional morphisms, where $\mathscr Q$ is a commutative semicartesian quantale. We describe, in detail, the limits and colimits of this complete and…
We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
We introduce a class of diffeological spaces, called elastic, on which the left Kan extension of the tangent functor of smooth manifolds defines an abstract tangent functor in the sense of Rosicky. On elastic spaces there is a natural…
In this article we present ways to evaluate certain sums, products and continued fractions using tools from the theory of elliptic functions. The specific results appear to be new, although similar ones can be found in the leterature; in…
Pippenger's Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set $A$ and taking values in a possibly different set $B$, where any…
In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new…
Refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type…
We define a category with as objects operational resolutions and with as morphisms - not necessarily deterministic - state transitions. We study connections with closure spaces and join-complete lattices and sketch physical applications…
We give a categorical explanation for many properties of profinite coproducts of profinite groups, which were previously proven on a case-by-case basis. All of these properties take the form "certain functors preserve profinite coproducts".…
It is investigated how graded variants of integral and complete integral closures behave under coarsening functors and under formation of group algebras.
We relate invariants in derived categories associated to tame actions of finite groups on projective varieties over a finite field to zeros of L-functions
We state a Yoneda-type lemma which leads to various functor categories being compact closed.
We thoroughly treat several familiar and less familiar definitions and results concerning categories, functors and distributors enriched in a base quantaloid Q. In analogy with V-category theory we discuss such things as adjoint functors,…
Given a scheme S and a flat morphism T \to S of finite presentation we define a surjective S-morphism to an {\'e}tale and separated S-scheme, which is universal in an obvious sense. Properties of this morphism are deduced from a thorough…
To a Lie groupoid over a compact base, the associated group of bisection is an (infinite-dimensional) Lie group. Moreover, under certain circumstances one can reconstruct the Lie groupoid from its Lie group of bisections. In the present…