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ADHESIVE AND QUASIADHESIVE CATEGORIES
 THEORETICAL INFORMATICS AND APPLICATIONS
, 1999
"... We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are wellbehaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be ex ..."
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Cited by 37 (3 self)
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We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are wellbehaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Doublepushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.
Functorial Factorization, Wellpointedness and Separability
"... A functorial treatment of factorization structures is presented, under extensive use of wellpointed endofunctors. Actually, socalled weak factorization systems are interpreted as pointed lax indexed endofunctors, and this sheds new light on the correspondence between reflective subcategories and f ..."
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Cited by 14 (4 self)
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A functorial treatment of factorization structures is presented, under extensive use of wellpointed endofunctors. Actually, socalled weak factorization systems are interpreted as pointed lax indexed endofunctors, and this sheds new light on the correspondence between reflective subcategories and factorization systems. The second part of the paper presents two important factorization structures in the context of pointed endofunctors: concordantdissonant and inseparableseparable.
Toposes are adhesive
 In International Conference on Graph Tranformation, icgt’06, volume 4178 of Lect. Notes Comput. Sc
, 2006
"... Abstract. Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that ..."
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Cited by 7 (2 self)
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Abstract. Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that toposes are adhesive. The proof relies on exploiting the relationship between adhesive categories, Brown and Janelidze’s work on generalised van Kampen theorems as well as Grothendieck’s theory of descent.
Factorization Systems For Symmetric CatGroups
 THEORY AND APPLICATIONS OF CATEGORIES, PREPRINT
, 2000
"... This paper is a first step in the study of symmetric catgroups as the 2dimensional analogue of abelian groups. We show that a morphism of symmetric catgroups can be factorized as an essentially surjective functor followed by a full and faithful one, as well as a full and essentially surjective fu ..."
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Cited by 6 (0 self)
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This paper is a first step in the study of symmetric catgroups as the 2dimensional analogue of abelian groups. We show that a morphism of symmetric catgroups can be factorized as an essentially surjective functor followed by a full and faithful one, as well as a full and essentially surjective functor followed by a faithful one. Both these factorizations give rise to a factorization system, in a suitable 2categorical sense, in the 2category of symmetric catgroups. An application to exact sequences is given.
Internal monotonelight factorization for categories via preorders
 Theory Appl. Categories
"... ..."
QUANTUM GAUGE FIELD THEORY IN COHESIVE HOMOTOPY TYPE THEORY
"... Abstract. We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge field theory. This is a brief survey of work by th ..."
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Abstract. We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge field theory. This is a brief survey of work by the authors developed in detail elsewhere [48, 45]. Contents
BOOLEAN GALOIS THEORIES
"... Abstract. We develop a general approach to adjunctions satisfying the admissibility condition useful for Boolean Galois Theories, i. e. for Galois Theories whose Galois (pre)groupoids are profinite. Various examples and applications are briefly described. ..."
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Abstract. We develop a general approach to adjunctions satisfying the admissibility condition useful for Boolean Galois Theories, i. e. for Galois Theories whose Galois (pre)groupoids are profinite. Various examples and applications are briefly described.
On the monad of proper factorisation systems in categories ( *)
, 2001
"... Abstract. It is known that factorisation systems in categories can be viewed as unitary pseudo algebras for the monad (–) 2, in Cat. We show in this note that an analogous fact holds for proper (i.e., epimono) factorisation systems and a suitable quotient of the former monad, deriving from a constru ..."
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Abstract. It is known that factorisation systems in categories can be viewed as unitary pseudo algebras for the monad (–) 2, in Cat. We show in this note that an analogous fact holds for proper (i.e., epimono) factorisation systems and a suitable quotient of the former monad, deriving from a construct introduced by P. Freyd for stable homotopy. Structural similarities of the previous monad with the path endofunctor of topological spaces are considered.
SEVERAL CONSTRUCTIONS FOR FACTORIZATION SYSTEMS DALI ZANGURASHVILI
"... Abstract. The paper develops the previously proposed approach to constructing factorization systems in general categories. This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) "reflects"factorization system ..."
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Abstract. The paper develops the previously proposed approach to constructing factorization systems in general categories. This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) &quot;reflects&quot;factorization systems. In particular, a generalization of the wellknown CassidyH'ebertKelly factorization theorem is given. The problem of relating a factorization system toa pointed endofunctor is considered. Some relevant examples in concrete categories are given. 1. Introduction The problem of relating a factorization system on a category C to an adjunction C I / / XHoo, (1.1) was thoroughly considered by C. Cassidy, M. H'ebert and G. M. Kelly in [CHK]. The wellknown theorem of these authors states that in the case of a finitely wellcomplete category C the pair of morphism classes\Gamma