Completions of (small) categories under certain kinds of colimits and exactness conditions have been studied extensively in the literature. When the category that we complete is not left exact but has some weaker kind of limit for finite diagrams, the universal property of the completion is usually stated with respect to functors that enjoy a property reminiscent of flatness. In this fashion no...

2 Properties of Moduli Functors 22 2.1 Nilcomplete, Cohesive, and Integrable Functors . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Relativized Properties of Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3 Finiteness Conditions on Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.4 Moduli of Spectral Deligne-Mumford St...

1. Categories 2 1.1. First Definition and Examples 2 1.2. An Alternative Definition: The Arrows-Only Perspective 7 1.3. Some Constructions 8 1.4. The Category of Relations 9 1.5. Special Objects and Arrows 10 1.6. Exercises 14 2. Functors and Natural Transformations 16 2.1. Functors 16 2.2. Full and Faithful Functors 20 2.3. Contravariant Functors 21 2.4. Products of Categories 23 3. Natural Tr...

A quandle is an algebraic system with a binary operation satisfying three axioms modelled on the Reidemeister moves of planar diagrams links in 3-space. The paper establishes new relationship between cohomology, extensions and automorphisms quandles. We derive four term exact sequence relating 1-cocycles, second cohomology certain group abelian extension non-abelian counterpart this involving d...

The language of classical propositional iog-Ic is extended by functorial variables as a new syntactical category. Functorial variables render to be a possible integrating representation of both assertion and presup-position in one and the same logical formula different from such using classical conjunction. O~ Introduction From a computational point of vlew there is an important difficulty of a...

We study the category O for a general Coxeter system using a formulation of Fiebig. The translation functors, the Zuckerman functors and the twisting functors are defined. We prove the fundamental properties of these functors, the duality of Zuckerman functor and generalization of Verma’s result about homomorphisms between Verma modules.

2 Derived Functors 2 2.1 Classical Derived Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Localisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Bounded Derived Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Linear Derived Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

initiality Lutz Schröder, Horst Herrlich Abstract. We study morphisms that are initial w.r.t. all functors in a given conglomerate. Several results and counterexamples are obtained concerning the relation of such properties to different notions of subobject. E.g., strong monomorphisms are initial w.r.t. all faithful adjoint functors, but not necessarily w.r.t. all faithful monomorphism-preservi...

In this paper, I give several characterizations of rational biset functors over p-groups, which are independent of the knowledge of genetic bases for p-groups. I also introduce a construction of new biset functors from known ones, which is similar to the Yoneda construction for representable functors, and to the Dress construction for Mackey functors, and I show that this construction preserves...