Homotopical algebra is a branch of mathematics that studies algebraic structures and their relationships through the lens of homotopy theory. It combines ideas from algebra, topology, and category theory, and it is particularly concerned with the properties of mathematical objects that are invariant under continuous deformations (homotopies).
The term "H-object" may refer to different things depending on the context, but it is not a widely recognized term in mainstream science or technology as of my last knowledge update in October 2023.
A homotopy Lie algebra is an algebraic structure that arises in the context of homotopy theory, particularly in the study of spaces, their algebraic invariants, and the relationships between them. It generalizes the notion of a Lie algebra by allowing for "higher" homotopical information. ### Definition 1.
A presheaf with transfers is a concept in the realm of algebraic geometry and homotopy theory, specifically in the study of sheaves and cohomological constructs. The notion is related to the idea of "transfers," which are maps that allow for the extension of certain algebraic structures across various bases or schemes.
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