Ordinal invariants in topology
by Kannan, V.
fromMemoirs of the American Mathematical Society
In this work we show that almost all useful ordinal invariants in topology studied until now (such as derived length of scattered spaces, sequential order of sequential spaces, etc.) can be brought under the single heading of what we call the order of a map. This helps us to per…
S-modules in the category of schemes
by Hu, Po
fromMemoirs of the American Mathematical Society
A [italic]G-category is a category on which a group [italic]G acts. This work studies the 2-category [italic]G-cat of [italic]G-categories, [italic]G-functors (functors which commute with the action of [italic]G) and [italic]G-natural transformations (natural transformations whi…
This paper offers a systematic approach to all mathematical theories with local/global behavior. To build objects with local and global aspects, on begins with a category of [script]C of allowed local structures, and somehow derives a category [script]C[superscript]gl of things …
It is the goal of the memoir to develop a functorial transfer of properties between [italic capital]A and [script capital]M[subscript italic capital]E, the category of modules over [italic capital]E, that is more sensitive than the traditional starting point, Hom([italic capital…
If [italic]k is a commutative ring, the isomorphism classes of [italic]k-algebroids (small [italic]k categories) form a commutative monoid under the tensor product. Moreover, Morita equivalence is a congruence relation on this monoid. It is shown that the group of invertible ele…
![Elements of [infinity]-category theory](https://covers.openlibrary.org/b/isbn/9781108837989-M.jpg?default=false)
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might…
