Variations of the Shifting Lemma and Goursat categories

Shifting Lemma and shifting lattice identities

(I.Ch.:) Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic (G.Cz. and E.K.H.:) University of Szeged, Bolyai Institute, Szeged, Aradi vértanúk tere 1, HUNGARY–6720. E-mail: [email protected], [email protected], [email protected]

A New Characterisation of Goursat Categories

We present a new characterisation of Goursat categories in terms of special kind of pushouts, that we call Goursat pushouts. This allows one to prove that, for a regular category, the Goursat property is actually equivalent to the validity of the denormalised 3-by-3 Lemma. Goursat pushouts are also useful to clarify, from a categorical perspective, the existence of the quaternary operations cha...

On closure operators, reflections and protolocalisations in Goursat categories

By defining a closure operator on effective equivalence relations in a regular category C, it is possible to establish a bijective correspondence between these closure operators and the regular epireflective subcategories of C, on the model of the closure operators on kernels in homological categories [5]. When C is an exact Goursat category [6], this correspondence restricts to a bijection bet...

2-Categories and Yoneda lemma

A∞-categories and the Yoneda lemma

Let C be the differential graded category of differential graded k-modules. We prove that the Yoneda A ∞ -functor Y : A → A ∞ (A,C) is a full embedding for an arbitrary unital A ∞ -category A. For a differential graded k-quiver B we define the free A ∞ -category FB generated by B. The main result is that the restriction A ∞ -functor A ∞ (FB,A) → A1(B,A) is an equivalence, where objects of the l...