Related papers: A Tangent Category Alternative to the Fa\`a di Bru…
A method of constructing covariant differential calculi on a quantum homogeneous space is devised. The function algebra X of the quantum homogeneous space is assumed to be a left coideal of a coquasitriangular Hopf algebra H and to contain…
The contributions of this paper are twofold. Within the framework of Grothendieck's fibrational category theory, we present a web of fundamental 2-adjunctions surrounding the formation of the category of all small diagrams in a given…
Affine schemes can be understood as objects of the opposite of the category of commutative and unital algebras. Similarly, $\mathscr{P}$-affine schemes can be defined as objects of the opposite of the category of algebras over an operad…
The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…
Coherence is here demonstrated for sesquicartesian categories, which are categories with nonempty finite products and arbitrary finite sums, including the empty sum, where moreover the first and the second projection from the product of the…
In this paper we consider the construction of a free differential algebra as an extension of the extended Bargmann algebra in arbitrary dimensions. This is achieved by introducing a new Maurer-Cartan equation for a three-form gauge…
High-order derivatives of nested functions of a single variable can be computed with the celebrated Fa\`a di Bruno's formula. Although generalizations of such formula to multiple variables exist, their combinatorial nature generates an…
We introduce the new concept of cartesian module over a pseudofunctor $R$ from a small category to the category of small preadditive categories. Already the case when $R$ is a (strict) functor taking values in the category of commutative…
We consider colored operads and their actions on categories. As a special example we construct a cobordism category with a colored operad action arising from oriented planar arc diagrams. This is used to construct an invariant of oriented…
In this work, we study the notion of cofinal functor of $\infty$-bicategories with respect to the theory of partially lax colimits. The main result of this paper is a characterization of cofinal functors of $\infty$-bicategories via…
We construct a left semi-model category of "marked strict $\infty$-categories" for which the fibrant objects are those whose marked arrows satisfy natural closure properties and are weakly invertible. The canonical model structure on strict…
We construct a new cylinder object for semifree differential graded (dg) categories in the category of dg categories. Using this, we give a practical formula computing homotopy colimits of semifree dg categories. Combining it with the…
In this contribution, we aim to introduce and study L-fuzzy partition spaces and L-fuzzy closure system spaces in a categorical framework. Further, we present the concepts of coalgebras and dialgebras corresponding to a direct upper F…
In 2017, O. Deiser and C. Lasser obtained an explicit formula for the $n$-th derivative of the inverse tangent function. We calculate this derivative by a different method based on Fa\`a di Bruno's formula. Comparing the two results leads…
We investigate the categorical connection between Dialectica constructions, Kolmogorov problems, Veloso problems and Blass problems. We show that the work of Kolmogorov can be regarded as a bridge between Veloso's abstract notion of a…
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to…
One of the major advantages of $\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\infty$-categories. However, it is both subtle and crucial…
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…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
Fr\"olicher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as C^\infty(M,G) or \Diff(M), but also projective limits of Lie groups are in a…