TL;DR
This paper introduces bi-operads and develops their homotopy theory, including Bital-Sets and infinite-bi-operads, and explores a geometric framework based on spectra of distributive monochromatic bi-operads.
Contribution
It defines bi-operads and advances the homotopy theory of Bital-Sets and infinite-bi-operads, proposing a new geometric approach using spectra of bi-operads.
Findings
Established the concept of bi-operads.
Developed the homotopy theory for Bital-Sets and infinite-bi-operads.
Proposed a geometric framework based on spectra of bi-operads.
Abstract
We define the concept of a bi-operad. We develop the homotopy theory of "Bital-Sets" and of infinite-bi-operads. We develop a geometry of generalized schemes based on the spectra of distributive monochromatic bi-operads.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Mathematical and Theoretical Analysis