9,842 research outputs found
Koszul duality for locally constant factorization algebras
Generalising Jacob Lurie's idea on the relation between the Verdier duality
and the iterated loop space theory, we study the Koszul duality for locally
constant factorisation algebras. We formulate an analogue of Lurie's
"nonabelian Poincare duality" theorem (which is closely related to earlier
results of Graeme Segal, of Dusa McDuff, and of Paolo Salvatore) in a symmetric
monoidal stable infinity category carefully, using John Francis' notion of
excision. Its proof depends on our earlier study of the Koszul duality for
E_n-algebras. As a consequence, we obtain a Verdier type equivalence for
factorisation algebras by a Koszul duality construction.Comment: 32 pages. Section 2.0 slightly simplified, References updated.
Comments welcome
On factorisation systems for surjective quandle homomorphisms
We study and compare two factorisation systems for surjective homomorphisms
in the category of quandles. The first one is induced by the adjunction between
quandles and trivial quandles, and a precise description of the two classes of
morphisms of this factorisation system is given. In doing this we observe that
a special class of congruences in the category of quandles always permute in
the sense of the composition of relations, a fact that opens the way to some
new universal algebraic investigations in the category of quandles. The second
factorisation system is the one discovered by E. Bunch, P. Lofgren, A. Rapp and
D. N. Yetter. We conclude with an example showing a difference between these
factorisation systems.Comment: 14 page
Pushing forward matrix factorisations
We describe the pushforward of a matrix factorisation along a ring morphism
in terms of an idempotent defined using relative Atiyah classes, and use this
construction to study the convolution of kernels defining integral functors
between categories of matrix factorisations. We give an elementary proof of a
formula for the Chern character of the convolution generalising the
Hirzebruch-Riemann-Roch formula of Polishchuk and Vaintrob.Comment: 43 pages, comments welcom
Lax orthogonal factorisation systems
This paper introduces lax orthogonal algebraic weak factorisation systems on
2-categories and describes a method of constructing them. This method rests in
the notion of simple 2-monad, that is a generalisation of the simple
reflections studied by Cassidy, H\'ebert and Kelly. Each simple 2-monad on a
finitely complete 2-category gives rise to a lax orthogonal algebraic weak
factorisation system, and an example of a simple 2-monad is given by completion
under a class of colimits. The notions of KZ lifting operation, lax natural
lifting operation and lax orthogonality between morphisms are studied.Comment: 59 page
The heart of a combinatorial model category
We show that every small model category that satisfies certain size
conditions can be completed to yield a combinatorial model category, and
conversely, every combinatorial model category arises in this way. We will also
see that these constructions preserve right properness and compatibility with
simplicial enrichment. Along the way, we establish some technical results on
the index of accessibility of various constructions on accessible categories,
which may be of independent interest.Comment: 44 pages, LaTeX. v4: Extended version of final journal version. (Note
that material has been significantly reorganised since v3.
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