Extension categories and their homotopy
Extensions of hom-Lie algebras in terms of cohomology
We study (non-abelian) extensions of a given hom-Lie algebra and provide a geometrical interpretation of extensions, in particular, we characterize an extension of a hom-Lie algebra by another hom-Lie algebra and discuss the case where has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, Maurer-Cartan formula, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction...
Free -categories.
Higher dimensional Peiffer elements in simplicial commutative algebras.
Higher-dimensional algebra. VI: Lie 2-algebras.
Homological Criteria for Finiteness.
Homological perturbation theory and associativity.
Homologie cyclique, caractère de Chern et lemme de perturbation.
Homotopy classes of truncated resolutions.
Inverse limits and cohomology
Note on homotopy pullbacks in abelian categories
Octahedra and braids
On a connection with torsion zero
On a homology of algebras with unit
We present a very general construction of a chain complex for an arbitrary (even non-associative and non-commutative) algebra with unit and with any topology over a field with a suitable topology. We prove that for the algebra of smooth functions on a smooth manifold with the weak topology the homology vector spaces of this chain complex coincide with the classical singular homology groups of the manifold with real coefficients. We also show that for an associative and commutative algebra with unit...
On compact solvability of differentials of an elliptic differential complex.
On constructing resolutions over the polynomial algebras.
On the homology of mapping spaces
Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.
On the locally finite chain algebra of a proper homotopy type.
On the Novikov complex for rational Morse forms
On total homology