symmetric monoidal (∞,1)-category of spectra
symmetric monoidal (∞,1)-category of spectra
homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
A partial evaluation is an instruction to evaluate a formal expression? piecewise, without necessarily obtaining the final result.
For a simple example, the sum “” can be evaluated to “”, but also partially evaluated to “”.
Let be a monad on Set, and let be an algebra over . Given two elements , a partial evaluation from to is an element such that , and .
Equivalently, partial evaluations are the 1-simplices of the bar construction (considered as a simplicial set) of the algebra .
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Tobias Fritz and Paolo Perrone, Monads, partial evaluations, and rewriting. (arXiv)
Carmen Constantin?, Tobias Fritz, Paolo Perrone and Brandon Shapiro?, Partial evaluations and the compositional structure of the bar construction. (arXiv)
Paolo Perrone, Walter Tholen, Kan extensions are partial colimits, Applied Categorical Structures, 2022. (arXiv:2101.04531)
Last revised on May 6, 2022 at 09:50:48. See the history of this page for a list of all contributions to it.