A note on epimorphisms of compact Lawson semilattices.
A note on exactness and stability in homotopical algebra.
A note on exponentiation in regular locales
A note on frame distributions
A note on free regular and exact completions and their infinitary generalizations.
A note on generators in categories
A note on Girard quantales
A note on Hacque's cohomology of rings-groups and extensions of rings-groups by groups.
A note on model structures on arbitrary Frobenius categories
We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category such that the homotopy category of this model structure is equivalent to the stable category as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact (closed)...
A note on normal topological functors and extensions of transformations
A note on product structures on Hochschild homology of schemes
We extend the definition of Hochschild and cyclic homologies of a scheme over a commutative ring k to define the Hochschild homologies HH⁎(X/S) and cyclic homologies HC⁎(X/S) of a scheme X with respect to an arbitrary base scheme S. Our main purpose is to study product structures on the Hochschild homology groups HH⁎(X/S). In particular, we show that carries the structure of a graded algebra.
A note on -embeddings
A note on reflective subcategories defined by partial algebras
A note on ring epimorphisms and polynomial identities
A note on subobjects defined by limit construction
A note on tangent bundles in a category with a ring object.
A note on tensor products on the unit interval
A note on the exact completion of a regular category, and its infinitary generalizations.
A note on the generalized reflexion of Guitart and Lair
A note on the locally Hausdorff property