homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
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see also algebraic topology
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symmetric monoidal (∞,1)-category of spectra
The oidification of an A3-space/H-monoid?, or equivalently, a category internal to .
A H-category or A3-spaceoid is a category internal to the classical homotopy category of topological spaces Ho(Top), or in the homotopy category of pointed topological spaces.
For the time being see category object in an (infinity,1)-category#HCategoryTypes.
In homotopy type theory, a H-category or A3-spaceoid is a type with
For each , a type , whose elements are called arrows or morphisms.
For each , a morphism , called the identity morphism.
For each , a function
called composition, and denoted infix by , or sometimes .
For each and , we have the left unitor and the right unitor .
For each ,
we have the associator .
Last revised on August 30, 2022 at 18:22:26. See the history of this page for a list of all contributions to it.